Question

if -5 is a root of 2x2+px-15=0and roots of px2+x+k =0 are having equal roots find Pand k

Answer 1

Since , ( - 5 ) is a root of the eq. f(x) = 2x² + px - 15 = 0

∴ value of x = ( - 5 )

∴ f(-5) = 2 ( - 5 )² + p ( - 5 ) - 15 = 0

⇒ 50 - 5p - 15 = 0

⇒ 35 - 5p = 0

⇒ 5p = 35

⇒ p = 7

NOW, p = 7 ∴ px² + x + k = 0

                   ⇒ 7x² + x + k = 0

IN THIS EQUATION , a = 7 , b = 1 , c = k

∵ the roots are equal ∴ b² - 4ac = 0

                                   ⇒ ( 1 )² - ( 4 × 7 × k ) = 0

                                   ⇒ 1 - 28k = 0

                                  ⇒ 28k = 1

                                  ⇒ k = 1/28

∴ VALUE OF P = 7 AND VALUE OF K = 1 / 28