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If the product of the roots of the equation $x^{2} - 3 x + k = 10$ is -2 then the value of k is

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-2

-8

answer is C.

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Detailed Solution

Given quadratic equation is,

x^{2} - 3 x + k = 10

.
The product of the roots is -2.
We know that,
The standard form of a quadratic equation is

a x^{2} + bx + c = 0,

where

a, b c

are real numbers and

a \neq 0

.
And, product of the roots is given by

\frac{c}{a}

.
Now,

x^{2} - 3 x + k = 10

\Rightarrow x^{2} - 3 x + (k - 10) = 0

After comparing the equation

x^{2} - 3 x + (k - 10) = 0

with the standard form, we get,

a = 1, b = - 3, c = k - 10

Product of the roots

= \frac{c}{a}

⟹

- 2 = \frac{k - 10}{1}

⟹

k - 10 = - 2

⟹ k = - 2 + 10

∴ k = 8

∴

If the product of the roots of the equation

x^{2} - 3 x + k = 10

is -2 then the value of k is 8.
Hence, the correct option is 3.

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