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CBSE Class 10 Answered

If -5 is a root of the quadratic equation 2x^2+ px –15 = 0 and the quadratic equation p(x^2+ x)k = 0 has equal roots, find the value of k.
Asked by srijan1805 | 06 Mar, 2019, 12:46: PM
answered-by-expert Expert Answer
 
 
begin mathsize 16px style 2 straight x squared space plus space px space minus space 15 space equals space 0
minus 5 space is space straight a space root space of space the space given space Quadratic space Equation.
Put space straight x space equals space minus 5 space in space 2 straight x squared space plus space px space minus space 15 space equals space 0
rightwards double arrow 2 open parentheses negative 5 close parentheses squared space plus space straight p left parenthesis negative 5 right parenthesis space minus space 15 space equals space 0
rightwards double arrow 50 space minus space 5 straight p space minus space 15 space equals space 0
rightwards double arrow 35 space equals space 5 straight p
rightwards double arrow straight p space equals space 7
We space have space straight p left parenthesis straight x squared space plus space straight x space right parenthesis space straight k space equals space 0 space
rightwards double arrow 7 left parenthesis straight x squared space plus space straight x space right parenthesis space straight k space equals space 0 space space space space space since space straight p space equals space 7
rightwards double arrow straight x squared straight k space plus space xk space space plus space 0 equals space 0
straight p left parenthesis straight x squared space plus space straight x space right parenthesis space straight k space equals space 0 space has space equal space roots space mean space straight b squared minus space 4 ac space equals space 0
rightwards double arrow straight k squared space minus space 4 left parenthesis straight k right parenthesis space cross times space 0 space equals space 0
rightwards double arrow straight k squared space equals space 0
rightwards double arrow straight k space equals space 0





end style
Answered by Yasmeen Khan | 06 Mar, 2019, 02:47: PM
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