The number of polynomials having zeros as 2 and 5 is

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More than 3

answer is D.

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Detailed Solution

Given, the zeros of the polynomial are -2 and 5.
Here the polynomial is of the form
p(x) = ax² + bx + c
We know that
Sum of zeros = – (coefficient of x) ÷ coefficient of x² = -

\frac{b}{a}

-2 + 5 = -

\frac{b}{a}

3 = -

\frac{b}{a}

b = -3 and a = 1
Product of the zeros = constant term ÷ coefficient of x² =

\frac{c}{a}

\frac{c}{a}

= (-2)(5)
c = -10
Now let us substitute a, b and c values in p (x)
x² - (3x) + (-10)
x² - 3x - 10
Therefore, the number of polynomials having zeros as -2 and 5 is more than 3.

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