Question

Write a polynomial whose zeroes are 2 and -7

Answer 1

ANSWER:

• Required polynomial = x²+5x-14

GIVEN:

• First zero (α) = 2
• Second zero (β) = -7

TO FIND:

• Polynomial whose zeroes are 2 and -7.

SOLUTION:

Standard form of Quadratic polynomial when Zeros are given:

= x²-(α+β)x+αβ. ....(i)

Finding sum of zeros (α+β) :

=> α = 2

=> β = (-7)

=> α+β = 2+(-7)

=> α+β = (-5)

Finding product of zeros (αβ)

=> αβ = 2(-7)

=> αβ = (-14)

Putting the values in eq (i) we get;

= x²-(-5)x+(-14)

= x²+5x-14

NOTE:

Some important formulas:

=> Sum of zeros (α+β) = -(Coefficient of x)/Coefficient of x²

=> Product of zeros (αβ) = Constant term/ Coefficient of x²

Answer 2

$\huge\mathfrak\green{Answer:}$

Given:

We have been given that the two zeroes of a polynomial are 2 and -7.

To Find:

We need to find the polynomial.

Solution:

As two zeroes of the polynomial are given,

=> Sum of zeroes(α + β)

= 2 + (-7)

= 2 - 7

= -5

=> Product of zeroes (αβ)

= 2 × (-7)

= -14

Now, we can find the polynomial by this formula:

k[ x^2 - (α + β)x + (αβ)]

substituting the values, we have

k[x^2 - (-5)x + (-14)]

= k[ x^2 + 5x - 14]

Hence the required polynomial is x^2 + 5x - 14.