Question

Write the quadratic polinomial whose zeros are 3,-5

Answer 1

ANSWER:

• Required polynomial = x²+2x-15

GIVEN:

• First zero (α) = 3
• Second zero (β) = (-5)

TO FIND:

• A quadratic polynomial.

SOLUTION:

Quadratic polynomial when zeros are given.

x²-(α+β)x+αβ

Finding sum of zeros (α+β)

= 3+(-5)

= (-2)

Finding product of zeros (αβ)

= 3(-5)

= (-15)

Putting these values we get;

= x²-(-2)x+(-15)

= x²+2x-15

NOTE:

some important formulas:

• (a+b)² = a²+b²+2ab
• (a-b)² = a²+b²-2ab
• (a+b)³ = a³+b³+3ab(a+b)
• (a-b)³ = a³-b³-3ab(a-b)