Find the roots of the quadratic equation $- x^{2} + 7 x - 10 = 0$ using the quadratic formula.

3, -5

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3, 4

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5, 6

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2, 5

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Solution

The correct option is D
2, 5

Given equation is $- x^{2} + 7 x - 10 = 0.$

On comparing with $a x^{2} + b x + c = 0$ , we get

a = -1, b = 7 and c = -10

By quadratic formula,

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$\Rightarrow x = \frac{- (7) \pm \sqrt{(7)^{2} - 4 (- 1) (- 10)}}{2 (- 1)}$

$\Rightarrow x = \frac{- 7 \pm \sqrt{49 - 40}}{- 2}$

$\Rightarrow x = \frac{- 7 \pm \sqrt{9}}{- 2}$

$\Rightarrow x = \frac{- 7 \pm 3}{- 2} = \frac{- 4}{- 2}, \frac{- 10}{- 2} = 2, 5$

So, 2 and 5 are two roots of the given equation.

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