Question

find the discriminate and the nature of roots
6x^2+7x-10=0​

Answer 1

EXPLANATION.

Discriminant and the nature of roots.

⇒ 6x² + 7x - 10 = 0.

As we know that,

⇒ D = Discriminant  Or  b² - 4ac.

⇒ D = (7)² - 4(6)(-10).

⇒ D = 49 + 240.

⇒ D = 289.

Nature of roots are real and  unequal Or  D > 0.

                                                                                                               

MORE INFORMATION.

Nature of the factors of the quadratic expression.

(1) = Real and different, 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 2

6x2 + 7x - 10 = 0

6x2 + 12x - 5x - 10 = 0

6x (x + 2) - 5x + 2) = 0

(6x - 5) (x + 2) = 0

X = -2,

$\frac{5}{6}$