Question

Find a quadratic polynomial, the sum and product of whose zeroes are - 7 and 2, respectively ?



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Answer 1

$\huge\bold{Answer:-}$

Given:-

• The sum of the zeroes are -7
• The product of the zeroes are 2

To Find:-

• The quadratic polynomial

Solution:-

We Know ,

To find a polynomial whose product of zeros and sum of zeroes are given , we use

= k[ x² + ( α + β ) - (αβ) ] ( where, k = constant )

now,

the product of zeroes = αβ = $\dfrac{c}{a }$

= $\dfrac{constant \:term }{coefficient \:of \:x²}$

= 2

The sum of zeroes = α + β = $\dfrac{-b}{a}$

= $\dfrac{-Coefficients \:of \:x }{coefficient \:of \:x²}$

= -7

so, the required polynomial becomes

= k[ x² + ( α + β ) - (αβ) ]

= k [ x² + ( -7 ) - ( 2) ]

= k [ x² - 7 - 2 ]

Therefore , the quadratic polynomial is x² - 7 - 2 .

Answer 2

Here is your answer ⤴️⬆️