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