Question

find the zeroes of quadratic polynomial 4√5xsquare -17x-3√5​

Answer 1

EXPLANATION.

Zeroes of the quadratic equation,

⇒ F(x) = 4√5x² - 17x - 3√5.

As we know that.

Factorizes the equation into middle term split, we get.

⇒ 4√5x² - 17x - 3√5 = 0.

⇒ 4√5x² - 12x - 5x - 3√5 = 0.

⇒ 4x(√5x - 3) + √5(√5x - 3) = 0.

⇒ (4x + √5)(√5x - 3) = 0.

⇒ x = -√5/4  and  x = 3/√5.

                                                                                         

MORE INFORMATION.

Relation between Roots and coefficients.

(1) = (α - β) = √(α + β)² - 4αβ = ±√b² - 4ac/a = ±√D/a.

(2) = α² + β² = (a + β)² - 2αβ = b² - 2ac/a².

(3) = α² - β² = (α + β)√(α + β)² - 4αβ = -b√b² - 4ac/a² = ±√D/a.

(4) = α³ + β³ = (α + β)³ - 3αβ(α + β) = -b(b² - 3ac)/a³.

(5) = α³ - β³ = (α + β)³ + 3αβ(α - β) = √(α + β)² - 4αβ = (b² - ac)√b² - 4ac/a³.

Answer 2

Zeroes of the quadratic equation,

⇒ F(x) = 4√5x² - 17x - 3√5.

As we know that.

Factorizes the equation into middle term split, we get.

⇒ 4√5x² - 17x - 3√5 = 0.

⇒ 4√5x² - 12x - 5x - 3√5 = 0.

⇒ 4x(√5x - 3) + √5(√5x - 3) = 0.

⇒ (4x + √5)(√5x - 3) = 0.

⇒ x = -√5/4  and  x = 3/√5.

                                                                                         

MORE INFORMATION.

Relation between Roots and coefficients.

(1) = (α - β) = √(α + β)² - 4αβ = ±√b² - 4ac/a = ±√D/a.

(2) = α² + β² = (a + β)² - 2αβ = b² - 2ac/a².

(3) = α² - β² = (α + β)√(α + β)² - 4αβ = -b√b² - 4ac/a² = ±√D/a.

(4) = α³ + β³ = (α + β)³ - 3αβ(α + β) = -b(b² - 3ac)/a³.

(5) = α³ - β³ = (α + β)³ + 3αβ(α - β) = √(α + β)² - 4αβ = (b² - ac)√b² - 4ac/a³