Question

If the roots of a quadratic equation are -4 and 3, then find the equation.

Answer 1

EXPLANATION.

Roots of the quadratic equation = - 4 and 3.

As we know that,

Sum of the zeroes of the quadratic polynomial.

⇒ α + β = - b/a.

⇒ - 4 + 3 = - 1.

⇒ α + β = - 1.

Products of the zeroes of the quadratic polynomial.

⇒ αβ = c/a.

⇒ (-4) x (3) = - 12.

⇒ αβ = - 12.

As we know that,

Formula of quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the value in the equation, we get.

⇒ x² - (-1)x + (-12).

⇒ x² + x - 12.

                                                                                                                       

MORE INFORMATION.

Conjugate roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

α = – 4 , β = 3

Sum of roots = (α + β)

= – 4 + 3

= – 12

Product of roots = α . β

= – 4 × 3

= – 12

x² + (sum of root) x + (Product of root) = 0

x² + ( – 1 ) x + ( – 12 ) = 0

$\fbox\red{ Answer = \: x² – x – 12}$