find the quadratic polynomial whose zeroes are 5 and -3
Answers
Answered by
5
EXPLANATION.
Quadratic polynomial whose zeroes are 5 and - 3.
As we know that,
Sum of the zeroes of quadratic polynomial.
⇒ α + β = - b/a.
⇒ 5 + (-3) = 2.
⇒ α + β = 2.
Products of the zeroes of quadratic polynomial.
⇒ αβ = c/a.
⇒ (5) x (-3) = - 15.
⇒ αβ = - 15.
As we know that,
Formula of quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (2)x + (- 15).
⇒ x² - 2x - 15 = 0.
MORE INFORMATION.
Nature of the roots of quadratic expression.
(1) Roots are real and unequal, if b² - 4ac > 0.
(2) Roots are rational and different, if b² - 4ac is a perfect square.
(3) Roots are real and equal, if b² - 4ac = 0.
(4) If D < 0 Root are imaginary and unequal Or complex conjugate.
Similar questions