What is the difference in the roots of the equation $x^{2} - 10 x + 9 = 0$ ?

2

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3

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5

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8

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Solution

The correct option is D $8$
We know that ${(p + q)}^{2} - 4 p q = {(p - q)}^{2}$
Let $p, q$ be the roots for equation $x^{2} - 10 x + 9 = 0$
Then $(p + q) = - (- 10) / 1 = 10$ and
Product of roots is $p q = 9 / 1 = 9$

Then $(p - q) = \sqrt{{(p + q)}^{2} - 4 p q} = \sqrt{10^{2} - 4 \times 9} = \sqrt{100 - 36} = \sqrt{64} = 8$
So, Difference of roots is $(p - q) = 8$
Hence, option D is correct.

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What is the difference in the roots of the equation x2−10x+9=0?

The correct option is D 8We know that (p+q)2−4pq=(p−q)2Let p,q be the roots for equation x2−10x+9=0Then (p+q)=−(−10)/1=10 andProduct of roots is pq=9/1=9 Then (p−q)=√(p+q)2−4pq=√102−4×9=√100−36=√64=8So, Difference of roots is (p−q)=8Hence, option D is correct.

What is the difference in the roots of the equation $x^{2} - 10 x + 9 = 0$ ?