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Mathematics

Assertion (A) : For quadratic equation 2x2 + 6x + 3 = 0, roots are real and equal.

Reason (R) : If for a quadratic equation ax2 + bx + c = 0, where a, b and c ∈ R and a = 0, then if discriminant > 0 and perfect square, implies roots of the quadratic equation are real, distinct and rational.

  1. A is true, R is false.

  2. A is false, R is true.

  3. Both A and R are true.

  4. Both A and R are false.

Quadratic Equations

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Answer

Given,

Equation : 2x2 + 6x + 3 = 0

Comparing above equation with ax2 + bx + c = 0, we get :

a = 2, b = 6 and c = 3.

By formula,

Discriminant (D) = b2−4ac\sqrt{b^2 - 4ac}

Substituting values we get :

D=62−4×2×3=36−24=12=23.D = \sqrt{6^2 - 4 \times 2 \times 3} \\[1em] = \sqrt{36 - 24} \\[1em] = \sqrt{12} \\[1em] = 2\sqrt{3}.

Since, D > 0.

∴ Roots are real and unequal.

∴ Assertion (A) is false.

In equation ax2 + bx + c = 0, if a = 0

Then the equation is not a quadratic equation.

∴ Reason (R) is false.

Hence, Option 4 is the correct option.

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