Question

solve the quadratic
eqation by complete
square method
5x^2+11x+6=0​

Answer 1

EXPLANATION.

Quadratic equation ⇒ 5x²+11x+6=0.

By using the middle term split.

⇒ 5x²+6x+5x+6=0.

⇒ x(5x+6)+1(5x+6) = 0.

⇒ ( x + 1 ) ( 5x + 6 ) = 0.

⇒ x = -1   and  x = -6/5.

                     

more information.

(1) = D > 0  or b²-4ac > 0  roots are real and unequal.

(2)= D = 0 or b²-4ac = 0 roots are real and equal.

(3) = D < 0 or b²-4ac < 0 roots are imaginary

(4) = quadratic equation whose roots are α and β.

•        sum of zeroes of quadratic equation
• α+β = -b/a
• product of zeroes of quadratic equation
• αβ = c/a.
• quadratic polynomial = x²-(α+β)x +αβ = 0.

(5) = quadratic equation whose zeroes are α,β,γ

• sum of zeroes of cubic polynomial
• α+β+γ = -b/a
• product of cubic polynomial two at a time
• αβ+βγ+γα = c/a.
• product of zeroes of cubic polynomial
• αβγ = -d/a.

Answer 2

5x²+11x+6

5x²+(6+5)x+6

5x²+6x+5x+6

x(5x+6)+1(5x+6)

(x+1)(5x+6)

x = -1 n x = -6/5