Question

If α and β are zeros of the p(x)= x^2– 8x + 5, then find a quadratic polynomials whose zeros are (α + 1) and (β + 1)

Answer 1

In the above question , the following information is given -

α and β are zeros of the p(x)= x²– 8x + 5 .

To find -

Find a quadratic polynomials whose zeros are (α + 1) and (β + 1) .

Solution -

Here ,

α and β are zeros of the p(x)= x²– 8x + 5 .

Now ,

α + β = ( -b / a ) = 8

α β = 5.

Now , zeroes of the new polynomial -

=> (α + 1) and (β + 1) .

Sum of zeroes -

=> α + 1 + β + 1

=> ( α + β ) + 2

=> 8 + 2

=> 10

Product of zeroes -

=> (α + 1) × (β + 1) .

=> α β + α + β + 1

=> 5 + 8 + 1

=> 14

Required polynomial -

=> x² - ( Sum of zeroes ) x + ( Product of zeroes )

=> x² - 10x + 14 .

This is the answer .

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