Find the quadratic polynomial whose zeros are -3 and 4
Answers
EXPLANATION.
Quadratic equation.
Zeroes are = -3 and 4.
As we know that,
Sum of the zeroes of the quadratic equation.
⇒ α + β = -b/a.
⇒ α + β = - 3 + 4 = 1.
Product of the zeroes of the quadratic equation.
⇒ αβ = c/a.
⇒ αβ = (-3)(4) = -12.
As we know that,
Formula of the quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (1)x + (-12) = 0.
⇒ x² - x - 12 = 0.
MORE INFORMATION.
Nature of the roots of the quadratic expression.
(1) = Real and unequal, if b² - 4ac > 0.
(2) = Rational and different, if b² - 4ac is a perfect square.
(3) = Real and equal, if b² - 4ac = 0.
(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.
Answer:
Hey mate your answer is as follows
Quadratic equation.
Quadratic equation Zeroes are = -3 and 4.
We know that
_____________________________
Sum of the zeroes of the quadratic equation.
Sum of the zeroes of the quadratic equation.⇒ α + β = -b/a.
Sum of the zeroes of the quadratic equation.⇒ α + β = -b/a.⇒ α + β = - 3 + 4 = 1.
______________________________
Product of the zeroes of the quadratic equation.
Product of the zeroes of the quadratic equation.⇒ αβ = c/a.
Product of the zeroes of the quadratic equation.⇒ αβ = c/a.⇒ αβ = (-3)(4) = -12.
______________________________
Formula of the quadratic polynomial.
Formula of the quadratic polynomial.⇒ x² - (α + β)x + αβ.
_______________________________
By Putting the values in the equation, we get.
the values in the equation, we get.⇒ x² - (1)x + (-12) = 0.
the values in the equation, we get.⇒ x² - (1)x + (-12) = 0.⇒ x² - x - 12 = 0.
_______________________________
hope it helps you.