Question

determine the values of p for which the quadratic equation px^2 + 8x + 1 = 0 has real roots.

Answer 1

EXPLANATION.

Quadratic equation.

⇒ px² + 8x + 1 = 0.

As we know that,

⇒ D = Discriminant Or b² - 4ac.

For real and equal roots : D = 0.

⇒ (8)² - 4(p)(1) = 0.

⇒ 64 - 4p = 0.

⇒ 4p = 64.

⇒ p = 16.

                                                                                                                         

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and unequal, if b² - 4ac > 0.

(2) = Real 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

Step-by-step explanation:

EXPLANATION.

Quadratic equation.

⇒ px² + 8x + 1 = 0.

As we know that,

⇒ D = Discriminant Or b² - 4ac.

For real and equal roots : D = 0.

⇒ (8)² - 4(p)(1) = 0.

⇒ 64 - 4p = 0.

⇒ 4p = 64.

⇒ p = 16.

                                                                                                                         

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and unequal, if b² - 4ac > 0.

(2) = Real 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.

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