Question

write the quadratic polynomial if its zeroes are smallest prime number and smallest​

Answer 1

Answer:

Smallest prime number is 2 and smallest composite number is 4.

Clearly, 2 is a factor of 4, so their H.C.F. is 2.

Thus, the H.C.F. of the smallest prime number and the smallest composite number is 2.

⇒ Given zeros are α=2 and β=−6.

⇒ Sum of zeros =α+β=2+(−6)=−4

⇒ Product of zeros =α×β=2×(−6)=−12

⇒ Quadratic polynomial = x^2 −(α+β)x+(α×β)

⇒ Quadratic polynomial = x^2−(−4)x+(−12)

∴ Quadratic polynomial = x^2+4x−12

Answer 2

Concept:

The polynomial equations of degree two in one variable of type f(x) = ax² + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x). The roots of the quadratic equation are the values of x that fulfil the equation (α,β ).

It is a given that the quadratic equation has two roots. Roots might have either real or imaginary nature.

Given:

if its zeroes are smallest prime number and smallest​

Find:

Write the quadratic polynomial

Solution:

Smallest prime number is 2 and smallest composite number is 4.

Clearly, 2 is a factor of 4, so their H.C.F. is 2.

Thus, the H.C.F. of the smallest prime number and the smallest composite number is 2.

⇒ Given zeros are α=2 and β=−6.

⇒ Sum of zeros =α+β=2+(−6)=−4

⇒ Product of zeros =α×β=2×(−6)=−12

⇒ Quadratic polynomial = x² −(α+β)x+(α×β)

⇒ Quadratic polynomial = x²−(−4)x+(−12)

Therefore, Quadratic polynomial = x²+4x−12

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