Question

Which shows the correct substitution of the values a, b, and c from the equation –2 = –x + x2 – 4 into the quadratic formula?
Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 4) EndRoot Over 2(1) EndFraction
x = StartFraction negative 1 plus or minus StartRoot 1 squared minus 4 (negative 1)(negative 4) EndRoot Over 2(negative 1) EndFraction
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 4) EndRoot Over 2(1) EndFraction
x = StartFraction negative (negative 1) plus or minus StartRoot (negative 1) squared minus 4 (1)(negative 2) EndRoot Over 2(1) EndFraction

Answer 1

$Given \: Quadratic \: equation : \\-2 = - x + x^{2} - 4$

$\implies 0 = - x + x^{2} - 4 + 2$

$\implies x^{2} - x - 2 = 0$

/* Compare above equation with ax^{2}+bx+c = 0 , we get */

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

$Discreminant (D) = b^{2} - 4ac \\= (-1)^{2} -4 \times 1 \times (-2) \\= 1 + 8 \\= 9$

$\underline { \orange { Quadratic \: Formula: }}$

$x = \frac{ -b \pm \sqrt{D} }{2a} \\= \frac{ -(-1)\pm \sqrt{9} }{2 \times 1 } \\= \frac{1 \pm 3 }{2}$

$\implies x = \frac{1 + 3 }{2} \: Or \: x = \frac{1- 3 }{2}$

$\implies x = \frac{4}{2} \: Or \: x = \frac{-2 }{2}$

$\implies x = 2 \: Or \: x = -1$

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Answer 2

Answer:

It is D

Step-by-step explanation:

EDG 2021