Quadratic Formula PYQs
Overview
This page provides comprehensive Class 10 Maths Quadratic Formula PYQs | Quadratic Equations. Quadratic Formula previous year questions for Class 10 Maths Quadratic Equations. Practice CBSE board PYQs with step-by-step solutions on SJMaths.
Practice Previous Year Questions Topic-wise
Q1
MCQ · 2025
00:00
If $\dfrac{x}{12}-\dfrac{3}{x}=0$, then the values of $x$ are:
Given equation: $\frac{x}{12}-\frac{3}{x}=0$
Taking LCM = $12x$
$x^2 - 36 = 0$
$x^2 = 36$
$x = \pm 6$
Final Answer: Option (a) ±6
Q2
SA-I · 2021–22
00:00
Solve the quadratic equation for $x$: $2x^2-2ax+(a^2-b^2)=0$
Given: $2x^2-2ax+(a^2-b^2)=0$
Factorising: $2x^2-2ax+a^2-b^2=0$
$(x-a)^2-b^2=0$
Using identity $A^2-B^2=(A-B)(A+B)$: $(x-a-b)(x-a+b)=0$
$x=a+b \text{ or } x=a-b$
Final Answer: $x=a+b$ or $x=a-b$
Q3
SA-I · 2021–22
00:00
Solve the quadratic equation: $x^2+2\sqrt2x-6=0$
Comparing with $ax^2+bx+c=0$: $a=1, b=2\sqrt2, c=-6$
Discriminant: $D=b^2-4ac=(2\sqrt2)^2+24=32$
$x=\frac{-b\pm\sqrt D}{2a}$
$x=\frac{-2\sqrt2\pm4\sqrt2}{2}$
$x=\sqrt2 \text{ or } x=-3\sqrt2$
Final Answer: $x=\sqrt2$ or $x=-3\sqrt2$
Q4
SA-II · 2023
00:00
Find the quadratic equation whose roots are $(3-\sqrt2)$ and $(3+\sqrt2)$.
Sum of roots: $\alpha+\beta=6$
Product of roots: $\alpha\beta=7$
Required equation: $x^2-(\alpha+\beta)x+\alpha\beta=0$
$x^2-6x+7=0$
Final Answer: $x^2-6x+7=0$
Q5
SA-II · 2016
00:00
Solve for $x$: $\frac{x-1}{x+1}+\frac{x+2}{x-2}=4$
Taking LCM $(x+1)(x-2)$
$(x-1)(x-2)+(x+2)(x+1)=4(x+1)(x-2)$
$2x^2-2x=4x^2-4x-8$
$x^2-x-4=0$
$x=\frac{1\pm\sqrt{17}}{2}$
Final Answer: $x=\dfrac{1\pm\sqrt{17}}{2}$
Q6
SA-II · Foreign 2016
00:00
Solve for $x$: $\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}, \; x\neq3,-5$
Taking LCM $(x-3)(x+5)$
$\frac{8}{(x-3)(x+5)}=\frac{1}{6}$
$48=(x-3)(x+5)$
$x^2+2x-63=0$
$(x+9)(x-7)=0$
$x=-9 \text{ or } x=7$
Final Answer: $x=7, -9$
Q7
SA-II · Foreign 2016
00:00
Solve for $x$: $\frac{a}{x-b}+\frac{b}{x-a}=2$
Taking LCM $(x-b)(x-a)$
$a(x-a)+b(x-b)=2(x-a)(x-b)$
$2x^2-3(a+b)x+(a+b)^2=0$
$x=\frac{3(a+b)\pm(a+b)}{4}$
Final Answer: $x=a+b$ or $x=\dfrac{a+b}{2}$
Q8
SA-II · Delhi 2016
00:00
Solve for $x$: $x^2+\left(\frac{a+b}{a}+\frac{a}{a+b}\right)x+1=0$
Let $\alpha=\frac{a+b}{a}$ and $\beta=\frac{a}{a+b}$
Then $\alpha\beta=1$
Equation becomes: $x^2+(\alpha+\beta)x+1=0$
Roots are $-\alpha$ and $-\beta$
Final Answer: $x=-\frac{a+b}{a}$ or $x=-\frac{a}{a+b}$
Q9
SA-II · AI 2019
00:00
Solve for $x$: $\frac{1}{a+b+x}=\frac{1}{a}+\frac{1}{b}+\frac{1}{x}$
Cross multiplying
$abx=(a+b+x)(ab+ax+bx)$
$x^2+(a+b)x=0$
$x(x+a+b)=0$
Final Answer: No valid solution
Q10
LA · 2021–22
00:00
Difference of squares is 180 and square of smaller is 8 times the greater. Find the numbers.
Let numbers be $x$ and $y$
$x^2-y^2=180, \; y^2=8x$
$x^2-8x-180=0$
$(x-18)(x+10)=0$
$x=18, y=12$
Final Answer: Numbers are 18 and 12
Q11
Application · 2024
00:00
Two digit number with product 36 and difference 5. Find the number.
$x(x-5)=36$
$x^2-5x-36=0$
$x=9$
Final Answer: Number is 94
Q12
Application · 2019
00:00
Sum of areas of two squares is 157 m² and sum of perimeters is 68 m. Find sides.
$x+y=17, x^2+y^2=157$
$xy=66$
$t^2-17t+66=0$
Final Answer: Sides are 11 m and 6 m
Q13
Solve-Type · 2021–22
00:00
Solve for $y$: $y^2+\frac{3\sqrt5}{2}y-5=0$
$D=\frac{125}{4}$
$y=\frac{-3\sqrt5\pm5\sqrt5}{4}$
Final Answer: $y=\frac{\sqrt5}{2}$ or $y=-2\sqrt5$
Q14
Solve-Type · 2021–22
00:00
Solve: $x^2-2ax+(a^2-b^2)=0$
$(x-a)^2-b^2=0$
$(x-a-b)(x-a+b)=0$
Final Answer: $x=a+b$ or $x=a-b$
Q15
Solve-Type · Foreign 2016
00:00
Solve: $\sqrt3x^2-2\sqrt2x-2\sqrt3=0$
$x^2-\frac{2\sqrt6}{3}x-2=0$
$x=\sqrt6, -\frac{\sqrt6}{3}$
Final Answer: $x=\sqrt6$ or $x=-\frac{\sqrt6}{3}$
If $\dfrac{x}{12}-\dfrac{3}{x}=0$, then the values of $x$ are:
Given equation: $\frac{x}{12}-\frac{3}{x}=0$
Taking LCM = $12x$
$x^2 - 36 = 0$
$x^2 = 36$
$x = \pm 6$
Final Answer: Option (a) ±6
Q2
SA-I · 2021–22
00:00
Solve the quadratic equation for $x$: $2x^2-2ax+(a^2-b^2)=0$
Given: $2x^2-2ax+(a^2-b^2)=0$
Factorising: $2x^2-2ax+a^2-b^2=0$
$(x-a)^2-b^2=0$
Using identity $A^2-B^2=(A-B)(A+B)$: $(x-a-b)(x-a+b)=0$
$x=a+b \text{ or } x=a-b$
Final Answer: $x=a+b$ or $x=a-b$
Q3
SA-I · 2021–22
00:00
Solve the quadratic equation: $x^2+2\sqrt2x-6=0$
Comparing with $ax^2+bx+c=0$: $a=1, b=2\sqrt2, c=-6$
Discriminant: $D=b^2-4ac=(2\sqrt2)^2+24=32$
$x=\frac{-b\pm\sqrt D}{2a}$
$x=\frac{-2\sqrt2\pm4\sqrt2}{2}$
$x=\sqrt2 \text{ or } x=-3\sqrt2$
Final Answer: $x=\sqrt2$ or $x=-3\sqrt2$
Q4
SA-II · 2023
00:00
Find the quadratic equation whose roots are $(3-\sqrt2)$ and $(3+\sqrt2)$.
Sum of roots: $\alpha+\beta=6$
Product of roots: $\alpha\beta=7$
Required equation: $x^2-(\alpha+\beta)x+\alpha\beta=0$
$x^2-6x+7=0$
Final Answer: $x^2-6x+7=0$
Q5
SA-II · 2016
00:00
Solve for $x$: $\frac{x-1}{x+1}+\frac{x+2}{x-2}=4$
Taking LCM $(x+1)(x-2)$
$(x-1)(x-2)+(x+2)(x+1)=4(x+1)(x-2)$
$2x^2-2x=4x^2-4x-8$
$x^2-x-4=0$
$x=\frac{1\pm\sqrt{17}}{2}$
Final Answer: $x=\dfrac{1\pm\sqrt{17}}{2}$
Q6
SA-II · Foreign 2016
00:00
Solve for $x$: $\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}, \; x\neq3,-5$
Taking LCM $(x-3)(x+5)$
$\frac{8}{(x-3)(x+5)}=\frac{1}{6}$
$48=(x-3)(x+5)$
$x^2+2x-63=0$
$(x+9)(x-7)=0$
$x=-9 \text{ or } x=7$
Final Answer: $x=7, -9$
Q7
SA-II · Foreign 2016
00:00
Solve for $x$: $\frac{a}{x-b}+\frac{b}{x-a}=2$
Taking LCM $(x-b)(x-a)$
$a(x-a)+b(x-b)=2(x-a)(x-b)$
$2x^2-3(a+b)x+(a+b)^2=0$
$x=\frac{3(a+b)\pm(a+b)}{4}$
Final Answer: $x=a+b$ or $x=\dfrac{a+b}{2}$
Q8
SA-II · Delhi 2016
00:00
Solve for $x$: $x^2+\left(\frac{a+b}{a}+\frac{a}{a+b}\right)x+1=0$
Let $\alpha=\frac{a+b}{a}$ and $\beta=\frac{a}{a+b}$
Then $\alpha\beta=1$
Equation becomes: $x^2+(\alpha+\beta)x+1=0$
Roots are $-\alpha$ and $-\beta$
Final Answer: $x=-\frac{a+b}{a}$ or $x=-\frac{a}{a+b}$
Q9
SA-II · AI 2019
00:00
Solve for $x$: $\frac{1}{a+b+x}=\frac{1}{a}+\frac{1}{b}+\frac{1}{x}$
Cross multiplying
$abx=(a+b+x)(ab+ax+bx)$
$x^2+(a+b)x=0$
$x(x+a+b)=0$
Final Answer: No valid solution
Q10
LA · 2021–22
00:00
Difference of squares is 180 and square of smaller is 8 times the greater. Find the numbers.
Let numbers be $x$ and $y$
$x^2-y^2=180, \; y^2=8x$
$x^2-8x-180=0$
$(x-18)(x+10)=0$
$x=18, y=12$
Final Answer: Numbers are 18 and 12
Q11
Application · 2024
00:00
Two digit number with product 36 and difference 5. Find the number.
$x(x-5)=36$
$x^2-5x-36=0$
$x=9$
Final Answer: Number is 94
Q12
Application · 2019
00:00
Sum of areas of two squares is 157 m² and sum of perimeters is 68 m. Find sides.
$x+y=17, x^2+y^2=157$
$xy=66$
$t^2-17t+66=0$
Final Answer: Sides are 11 m and 6 m
Q13
Solve-Type · 2021–22
00:00
Solve for $y$: $y^2+\frac{3\sqrt5}{2}y-5=0$
$D=\frac{125}{4}$
$y=\frac{-3\sqrt5\pm5\sqrt5}{4}$
Final Answer: $y=\frac{\sqrt5}{2}$ or $y=-2\sqrt5$
Q14
Solve-Type · 2021–22
00:00
Solve: $x^2-2ax+(a^2-b^2)=0$
$(x-a)^2-b^2=0$
$(x-a-b)(x-a+b)=0$
Final Answer: $x=a+b$ or $x=a-b$
Q15
Solve-Type · Foreign 2016
00:00
Solve: $\sqrt3x^2-2\sqrt2x-2\sqrt3=0$
$x^2-\frac{2\sqrt6}{3}x-2=0$
$x=\sqrt6, -\frac{\sqrt6}{3}$
Final Answer: $x=\sqrt6$ or $x=-\frac{\sqrt6}{3}$