Question

discuss the nature of roots of quadratic equation 3x²+2x-15=0​

Answer 1

EXPLANATION.

Nature of the quadratic equation,

⇒ 3x² + 2x - 15 = 0.

As we know that,

⇒ D = Discriminant.

⇒ D = b² - 4ac.

⇒ D = (2)² - 4(3)(-15).

⇒ D = 4 + 180.

⇒ D = 184.

⇒ 184 > 0. it means,

D > 0 Roots are real and unequal.

                                                                                                                   

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

Answer:

Roots of the quadratic equation are real and unequal.

Step-by-step explanation:

Nature of roots of quadratic equation :

• A Quadratic equation is of form ax² + bx + c =0
• The discriminant, D of the quadratic equation is (b² - 4ac).
• If discriminant, D > 0, the roots of the quadratic equation is real and unequal.
• If discriminant, D = 0, the roots of the quadratic equation is real and equal.
• If discriminant, D < 0, the roots of the quadratic equation is imaginary.

Given that :

• Quadratic equation is 3x² + 2x - 15 = 0.

Solution :

• Comparing the given quadratic equation with standard form, we get
• a = 3; b = 2; c = -15.
• Discriminant of the given quadratic equation is ((2)²-4(3)(-15)) = 4 + 180 = 184.
• Discriminant, D > 0.
• Hence, roots of the quadratic equation are real and unequal.