Question

If α = 5 and β = 9, then form the quadratic equation​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

EXPLANATION.

If α = 5  and  β = 9.

As we know that,

Sum of the zeroes of the quadratic expression.

⇒ α + β = - b/a.

⇒ 5 + 9 = 14.

Products of the zeroes of the quadratic expression.

⇒ αβ = c/a.

⇒ (5) x (9) = 45.

As we know that,

Formula of the quadratic expression.

⇒ x² - (α + β)x + αβ.

Put the values in the equation, we get.

⇒ x² - (14)x + (45).

⇒ x² - 14x + 45 = 0.

                                                                                                                   

MORE INFORMATION.

Nature of the roots of the 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 Roots are imaginary and unequal Or complex conjugate.