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Chapter 4: Quadratic Equations

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This page provides comprehensive Chapter 4: Quadratic Equations - MCQ Worksheet - SJMaths. Multiple Choice Questions (MCQ) worksheet for Class 10 Quadratic Equations. Practice for CBSE Board Exams.

MCQ Worksheet

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  1. Question 1: Which of the following is NOT a quadratic equation?
    (A) $(x-2)^2 + 1 = 2x - 3$
    (B) $x(x+1) + 8 = (x+2)(x-2)$
    (C) $x(2x+3) = x^2+1$
    (D) $(x+2)^3 = x^3 - 4$
    Solution: (B) $x(x+1) + 8 = (x+2)(x-2)$
    Step 1: Simplify LHS: $x^2 + x + 8$.
    Step 2: Simplify RHS: $x^2 - 4$.
    Step 3: $x^2 + x + 8 = x^2 - 4 \Rightarrow x + 12 = 0$. This is a linear equation.
  2. Question 2: The roots of the quadratic equation $x^2 - 0.04 = 0$ are:
    (A) $\pm 0.2$
    (B) $\pm 0.02$
    (C) $0.4$
    (D) $0.2$
    Solution: (A) $\pm 0.2$
    Step 1: $x^2 = 0.04$.
    Step 2: $x = \sqrt{0.04} = \pm 0.2$.
  3. Question 3: The discriminant of the quadratic equation $2x^2 - 4x + 3 = 0$ is:
    (A) -8
    (B) 8
    (C) 16
    (D) 24
    Solution: (A) -8
    Step 1: $D = b^2 - 4ac$. Here $a=2, b=-4, c=3$.
    Step 2: $D = (-4)^2 - 4(2)(3) = 16 - 24 = -8$.
  4. Question 4: If the equation $x^2 + 4x + k = 0$ has real and distinct roots, then:
    (A) $k < 4$
    (B) $k > 4$
    (C) $k \ge 4$
    (D) $k \le 4$
    Solution: (A) $k < 4$
    Step 1: For real and distinct roots, $D > 0$.
    Step 2: $b^2 - 4ac > 0 \Rightarrow 4^2 - 4(1)(k) > 0$.
    Step 3: $16 - 4k > 0 \Rightarrow 16 > 4k \Rightarrow k < 4$.
  5. Question 5: The nature of roots of the equation $2x^2 - \sqrt{5}x + 1 = 0$ is:
    (A) Real and distinct
    (B) Real and equal
    (C) No real roots
    (D) None of these
    Solution: (C) No real roots
    Step 1: Calculate $D = b^2 - 4ac$.
    Step 2: $D = (-\sqrt{5})^2 - 4(2)(1) = 5 - 8 = -3$.
    Step 3: Since $D < 0$, the equation has no real roots.
  6. Question 6: If one root of the equation $2x^2 + kx - 6 = 0$ is 2, then the value of $k$ is:
    (A) 1
    (B) -1
    (C) 2
    (D) -2
    Solution: (B) -1
    Step 1: Substitute $x=2$ in the equation.
    Step 2: $2(2)^2 + k(2) - 6 = 0 \Rightarrow 8 + 2k - 6 = 0$.
    Step 3: $2k + 2 = 0 \Rightarrow 2k = -2 \Rightarrow k = -1$.
  7. Question 7: The sum of the roots of the quadratic equation $3x^2 - 9x + 5 = 0$ is:
    (A) 3
    (B) -3
    (C) 5/3
    (D) -5/3
    Solution: (A) 3
    Step 1: Sum of roots $= -b/a$.
    Step 2: Here $a=3, b=-9$.
    Step 3: Sum $= -(-9)/3 = 9/3 = 3$.
  8. Question 8: Which of the following equations has 2 as a root?
    (A) $x^2 - 4x + 5 = 0$
    (B) $x^2 + 3x - 12 = 0$
    (C) $2x^2 - 7x + 6 = 0$
    (D) $3x^2 - 6x - 2 = 0$
    Solution: (C) $2x^2 - 7x + 6 = 0$
    Step 1: Substitute $x=2$ in option (C).
    Step 2: $2(2)^2 - 7(2) + 6 = 8 - 14 + 6 = 14 - 14 = 0$.
    Step 3: Since LHS = RHS, 2 is a root.
  9. Question 9: If the roots of $ax^2 + bx + c = 0$ are equal, then $c$ is equal to:
    (A) $-b/2a$
    (B) $b/2a$
    (C) $-b^2/4a$
    (D) $b^2/4a$
    Solution: (D) $b^2/4a$
    Step 1: For equal roots, $D = 0 \Rightarrow b^2 - 4ac = 0$.
    Step 2: $b^2 = 4ac$.
    Step 3: $c = b^2 / 4a$.
  10. Question 10: Values of $k$ for which the quadratic equation $2x^2 - kx + k = 0$ has equal roots is:
    (A) 0 only
    (B) 4
    (C) 8 only
    (D) 0, 8
    Solution: (D) 0, 8
    Step 1: For equal roots, $D = 0 \Rightarrow b^2 - 4ac = 0$.
    Step 2: $(-k)^2 - 4(2)(k) = 0 \Rightarrow k^2 - 8k = 0$.
    Step 3: $k(k-8) = 0 \Rightarrow k = 0$ or $k = 8$.
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