Question

1If α and β are the zeroes of a polynomial such that α + β = -7 and αβ = 10, then find the polynomial.

*Answer. ​

Answer 1

Answer :

x² + 7x + 10 is the required polynomial.

Explanation :

According to the Question

It is given that α and β are the zeroes of a polynomial .

• Sum of zeros (α+β) = -7
• Product of Zeros (αβ) = 10

we need to calculate the polynomial.

As we know that if the sum of zeros and product of zeros are given we can easily calculate the polynomial .

Let the Polynomial be P(x)

• P(x) = x²-(sum of zeros)x + (product of zeros)

Substitute the value we get

➻ P(x) = x²-(-7)x + (10)

➻ P(x) = x²+7x+10

• So, the required polynomial is x² + 7x + 10.

Answer 2

Given :-

If α and β are the zeroes of a polynomial such that α + β = -7 and αβ = 10

To Find :-

Polynomial

Solution :-

We know that

Standard form of a quadratic polynomial = x² - (α + β)x + αβ

Sum of zeroes = α + β

Sum of zeroes = - 7(i)

Product of zeroes = αβ

Product of zeroes = 10 (ii)

Now,

Putting value from i and ii

Polynomial = x² - (-7)x + (10)

Polynomial = x² + 7x + 10