Find the roots of the quadratic equations by using the quadratic formula in each of the following:
$ -x^{2}+7 x-10=0 $

Given:

Given quadratic equation is \( -x^{2}+7 x-10=0 \).

To do:

We have to find the roots of the given quadratic equation.

Solution:

$-x^2+7x - 10 = 0$

The above equation is of the form $ax^2 + bx + c = 0$, where $a = -1, b = 7$ and $c =-10$

Discriminant $\mathrm{D} =b^{2}-4 a c$

$=(7)^{2}-4 \times (-1)\times(-10)$

$=49-40$

$=9$

$\mathrm{D}>0$

Let the roots of the equation are $\alpha$ and $\beta$

$\alpha =\frac{-b+\sqrt{\mathrm{D}}}{2 a}$

$=\frac{-7+\sqrt{9}}{2(-1)}$

$=\frac{-7+3}{-2}$

$=\frac{-4}{-2}$

$=2$

$\beta =\frac{-b-\sqrt{\mathrm{D}}}{2 a}$

$=\frac{-7-\sqrt{9}}{2(-1)}$

$=\frac{-7-3}{-2}$

$=\frac{-10}{-2}$

$=5$

Hence, the roots of the given quadratic equation are $2, 5$. 

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Updated on: 10-Oct-2022

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