The equation $x^{2} + B x + C = 0$ has 5 as the sum of its roots and 15 as the sum of the square of its roots. The value of C is

5

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7.5

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10

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12.5

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Solution

The correct option is A $5$
Let the roots be $α$ and $β$
Hence
$α + β = 5$
And
$α^{2} + β^{2} = 15$
$(α + β)^{2} - 2 α . β = 15$
$25 - 2 α . β = 15$
$10 = 2 α . β$
Hence
$α . β = \frac{10}{2} = 5$
Now
Product of roots for an equation $a x^{2} + b x + c = 0$ is $= \frac{c}{a}$
Here $a = 1$ and $c = C$
Hence
$α . β = 5$
$= \frac{c}{a} = \frac{C}{1}$
$= C$
$∴ C = 5$

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The equation x2+Bx+C=0 has 5 as the sum of its roots and 15 as the sum of the square of its roots. The value of C is

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The equation $x^{2} + B x + C = 0$ has 5 as the sum of its roots and 15 as the sum of the square of its roots. The value of C is