Question:
Plz answer as soon as possible, I didnt understood the concept of quetions like this : If -5 is a root of the eqn 2x^2 px - 15 = 0 and quad eqn p(x^2 x) k = 0 has eql roots, find the value of k.
Answer:
Given -5 is a root of the equation 2x2 + px - 15 = 0
So, put x = -5 in the equation, we get
2(-5)2 + p*(-5) - 15 = 0
=> 2*25 - 5p - 15 = 0
=> 50 - 5p - 15 = 0
=> 35 - 5p = 0
=> 5p = 35
=> p = 35/5
=> p = 7
Now, put value of p in the equation p(x2 + x) + k = 0, we get
7(x2 + x) + k = 0
=> 7x2 + 7x + k = 0 ..............1
Given, this equation has equal roots,
So, its discriminant value shoul be eual to zero.
=> D = b2 - 4ac = 0 {if the equation is: ax2 + bx + c = 0}
=> 72 - 4*7*k = 0 from equation 1
=> 49 - 28k = 0
=> 28k = 49
=> k = 49/28
=> k = 7/4 (49 and 28 is divided by 7)
So, the value of k is 7/4
Hope you got the point.
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