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Mathematics

Assertion (A): The roots of the quadratic equation 8x2 + 2x - 3 = 0 are -12\dfrac{1}{2} and 34\dfrac{3}{4}.

Reason (R): The roots of the quadratic equation ax2 + bx + c = 0 are given by x=−b±b2−4ac2ax = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}.

  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,

⇒ 8x2 + 2x - 3 = 0

Comparing equation 8x2 + 2x - 3 = 0 with ax2 + bx + c = 0, we get :

a = 8, b = 2 and c = -3.

By formula,

x = −b±b2−4ac2a\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Substituting values we get :

⇒x=−(2)±(2)2−4×(8)×(−3)2×(8)=−2±4+9616=−2±10016=−2±1016=−2+1016 or −2−1016=816 or −1216=12 or −34.\Rightarrow x = \dfrac{-(2) \pm \sqrt{(2)^2 - 4 \times (8) \times (-3)}}{2 \times (8)} \\[1em] = \dfrac{-2 \pm \sqrt{4 + 96}}{16} \\[1em] = \dfrac{-2 \pm \sqrt{100}}{16} \\[1em] = \dfrac{-2 \pm 10}{16} \\[1em] = \dfrac{-2 + 10}{16} \text{ or } \dfrac{-2 - 10}{16} \\[1em] = \dfrac{8}{16} \text{ or } \dfrac{-12}{16} \\[1em] = \dfrac{1}{2} \text{ or } \dfrac{-3}{4}.

Thus, A is false, R is true.

Hence, option 2 is the correct option.

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