Question

Find the sum and product of zeros of the quadratic polynomial 3x square -4x+7

Answer 1

Given,

$The \: quadratic \: polynomial \: is \: {3x}^{2} - 4x + 7.$

To find out,

The sum and product of zeros of the polynomial.

Solution:

$quadratic \: polynomial = {3x}^{2} - 4x + 7$

$p(x) = {3x}^{2} - 4x + 7$

$The \: sum \: of \: zeroes \: of \: a \: quadratic \: polynomial \: ( \alpha + \beta ) = \frac{ - b}{a}$

$The \: product \: of \: zeroes \: of \: a \: quadratic \: polynomial \: ( \alpha \beta ) = \frac{c}{a}$

In the quadratic polynomial,

a = 3, b = -4, c = 7

$sum \: of \: zeroes \: = \frac{( - coefficient \: of \: {x)} }{(coefficient \: {x}^{2}) } = \frac{ - b}{a}$

$sum \: of \: zeroes \: = \frac{ - ( - 4)}{3}$

$\huge Therefore \: the \: sum \: of \: zeroes \: = \frac{4}{3}$

$product \: of \: zeroes \: = \frac{constant \: term}{coefficient \: of \: {x}^{2} } = \frac{c}{a}$

$\huge \: Therefore \: the \: product \: of \: zeroes \: is \: \frac{7}{3} .$

ADDITIONAL INFORMATION:

What is a quadratic polynomial?

● A polynomial whose degree is 2 is called as quadratic polynomial.

● Example:2x^2-2x+1

Answer 2

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