Solve by factorization.
⇒ 6x² + 7x - 10 = 0.
Factorize the equation into middle term splits, we get.
⇒ 6x² + 12x - 5x - 10 = 0.
⇒ 6x(x + 2) - 5(x + 2) = 0.
⇒ (6x - 5)(x + 2) = 0.
⇒ x = 5/6 and x = - 2.
Nature of the roots of 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.
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EXPLANATION.
Solve by factorization.
⇒ 6x² + 7x - 10 = 0.
Factorize the equation into middle term splits, we get.
⇒ 6x² + 12x - 5x - 10 = 0.
⇒ 6x(x + 2) - 5(x + 2) = 0.
⇒ (6x - 5)(x + 2) = 0.
⇒ x = 5/6 and x = - 2.
MORE INFORMATION.
Nature of the roots of 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.