Question

Find the quadratic polynomial sum and product of whose zeroes are -1 and -20 respectively.Also find the zeroes of the polynomial so obtained

please help me I will mark you brainliest​

Answer 1

your answer is in the attachment

Answer 2

$x^2-x-20 = 0$ is the quadratic polynomial whose sum and product of whose zeroes are -1 and -20

The zeros of the polynomial are -4 and 5

Solution:

The general quadratic equation is given as:

$x^2 - (\text{ sum of zeros })x + \text{ product of zeros }$

From given,

$\text{ sum of zeros } = -1\\\\\text{ product of zeros } = -20$

Therefore, quadratic polynomial is given as:

$x^2-x-20 = 0$

Find the zeros of the polynomial

$x^2-x-20 = 0\\\\\text{Split the middle term }\\\\x^2+4x-5x - 20 = 0\\\\\mathrm{Break\:the\:expression\:into\:groups}\\\\\left(x^2+4x\right)+\left(-5x-20\right)\\\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2+4x\\\\x(x + 4) + (-5x - 20)\\\\\mathrm{Factor\:out\:}-5\mathrm{\:from\:}-5x-20\\\\x(x + 4) - 5(x+4)\\\\\mathrm{Factor\:out\:common\:term\:}x+4\\\\\left(x+4\right)\left(x-5\right)$

$x + 4 = 0\\\\x = -4\\\\x - 5 = 0\\\\x = 5$

Thus zeros are -4 and 5

Learn more:

Find a quadratic polynomial,the sum and product of whose zeros are-8 and 12 respectively.hence find the zeros​

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Find the quadratic polynomial, sum of whose zeros is 8 and their product is 12. Hence find the zeros of the polynomial.

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