Question

Find a quadratic polynomial, the product and sum of whose zeros are 12
and 7 respectively. Hence, find the zeros of the polynomial.

Answer 1

Answer:

ok

Step-by-step explanation:

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Answer 2

The given question is we have to Find a quadratic polynomial, the product and sum of whose zeros are 12

and 7 respectively. Hence, find the zeros of the polynomial.

The sum of zeroes is 7

product of zeroes is 12

The general form of a quadratic polynomial is

${x}^{2} - x(sum of \: zeroes) + product \: of \: zeroes$

given

$\alpha + \beta =7 \\ \alpha \beta = 12$

substitute the above value in the equation

${x}^{2} - 7x + 12$The above equation is a required quadratic polynomial.

a=1 b=-7 c=12

$\frac{ (- b) + - \sqrt{ {b}^{2} - 4ac} }{2a}$

sub the above value in the formula, we get

$\frac{ - ( - 7) + - \sqrt{ {( - 7)}^{2} - 4 \times 1 \times 12 } }{2 \times 1}$

by proceeding further we get

$\frac{7 + - \sqrt{49 - 48} }{2}$

$\frac{7 + - \sqrt{1} }{2} \\ \frac{7 + 1}{2} and \frac{7 - 1}{2}$

$\frac{8}{2 } and \: \frac{6}{2}$

Therefore, the zeroes are 4 and 3 .

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