(C) quadratic polynomial with zeros $\alpha$ and $\beta$ is given by the formula: $p(x) = k[x^2 - (\alpha + \beta)x + (\alpha\beta)]$,where $k$ is a c

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(C) quadratic polynomial with zeros $\alpha$ and $\beta$ is given by the formula: $p(x) = k[x^2 - (\alpha + \beta)x + (\alpha\beta)]$,where $k$ is a constant.Given that the sum of the zeros $(\alpha + \beta) = -7$ and the product of the zeros $(\alpha\beta) = 12$.Substituting these values into the formula:$p(x) = x^2 - (-7)x + (12)$$p(x) = x^2 + 7x + 12$Thus,the correct option is $C$.

Class 10 Mathematics Polynomials Mix Examples - Polynomials

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If the sum of the zeros is $-7$ and the product of the zeros is $12$,then the quadratic polynomial is $\ldots \ldots \ldots$

A
$p(x) = x^2 - 7x + 12$
B
$p(x) = x^2 + 7x - 12$
C
$p(x) = x^2 + 7x + 12$
D
$p(x) = x^2 - 7x - 12$

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If the sum of the zeros is $-7$ and the product of the zeros is $12$,then the quadratic polynomial is $\ldots \ldots \ldots$

Similar Questions

Are the following statements 'True' or 'False'? Justify your answers.If all the zeroes of a cubic polynomial are negative,then all the coefficients and the constant term of the polynomial have the same sign.

For the quadratic polynomial $p(x) = ax^2 + bx + c$; if $a = 6$,$b = 11$,and $c = 4$,then the quadratic polynomial is..........

Draw the graph of $p(x) = x^3$ and find the zeros of this polynomial.

Find $k$ such that $x^{2}+2x+k$ is a factor of $2x^{4}+x^{3}-14x^{2}+5x+6$. Also,find all the zeroes of the two polynomials.

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Are the following statements 'True' or 'False'? Justify your answers.
If all the zeroes of a cubic polynomial are negative,then all the coefficients and the constant term of the polynomial have the same sign.