The number of polynomials having zeroes as -2 | vedclass

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(B) Let $p(x) = a(x^2 - (	ext{sum of zeroes})x + (	ext{product of zeroes}))$ be the general form of the polynomial.Given zeroes are $\alpha = -2$ an

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more than $3$

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(B) Let $p(x) = a(x^2 - (	ext{sum of zeroes})x + (	ext{product of zeroes}))$ be the general form of the polynomial.Given zeroes are $\alpha = -2$ and $\beta = 5$.Sum of zeroes $= \alpha + \beta = -2 + 5 = 3$.Product of zeroes $= \alpha \cdot \beta = -2 	imes 5 = -10$.Thus, the polynomial is of the form $p(x) = a(x^2 - 3x - 10)$, where $a$ is any non-zero real constant.Since $a$ can take any non-zero real value (e.g., $1, 2, 3, \dots, 0.5, \dots$), there are infinitely many such polynomials.Therefore, the number of such polynomials is more than $3$.

The number of polynomials having zeroes as $-2$ and $5$ is

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