Question

22. Find the zeroes of the quadratle polynomial x²– 3x – 10 and verify the relationship between
zeroes and coefficients​

Answer 1

Answer:

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Answer 2

ANSWER:

• Zeroes are 5 and (-2)

GIVEN:

• P(x) = x²-3x-10

TO FIND:

• Zeroes and verify the relationship between zeroes and coefficients.

SOLUTION:

=> x²-3x-10 = 0

=> x²-5x+2x-10 = 0

=> (x²-5x)+(2x-10) = 0

=> x(x-5)+2(x-5) = 0

=> (x-5)(x+2) = 0

Either (x-5) = 0

=> x = 5

Either (x+2) = 0

=> x = (-2)

Sum of zeroes:

= 5+(-2)

=> -(-3)/1 = -(Coefficient of x)/Coefficient of x²

Product of zeroes:

= 5(-2)

=> -10/1 = Constant term/ Coefficient of x²

Verified.

NOTE:

Some important formulas:

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

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