Question

Which shows the correct substitution of the values a, b, and c from the equation 0 = 4x2 + 2x – 1 into the quadratic formula below?

Use the Quadratic formula

Answer 1

4x2 + 2x – 1=0

a=4,b=2,c=-1

b^2-4ac

=(2)^2-4(4×-1)

=4-4(-4)

=4+16

=20

Answer 2

$Compare \: given \: Quadratic \: equation \\4x^{2}+2x-1 = 0 \: with \: ax^{2}+bx+c=0,we \:get$

$a = 4 , b = 2 \: and \: c = -1$

$i ) Discreminant (D) = b^{2} - 4ac \\= 2^{2} - 4 \times 4 \times (-1) \\= 4 + 16 \\= 20$

$\underline { \blue { Quadratic \: formula : }}$

$\boxed { \pink { x = \frac{-b\pm \sqrt{D}}{2a} }}$

$\implies x = \frac{ -2\pm \sqrt{20}}{2\times 4} \\= \frac{ -2\pm 2 \sqrt{5}}{8} \\= \frac{ 2(-1\pm \sqrt{5})}{8} \\= \frac{-1\pm \sqrt{5}}{4}$

Therefore.,

$\green { x = \frac{-1+ \sqrt{5}}{4}\:Or \: x = \frac{-1- \sqrt{5}}{4}}$

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