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Question

Question: The number of solutions for the equation \(x^{2} - 14x + 2a\) is....

The number of solutions for the equation

x214x+2ax^{2} - 14x + 2a is.

A

4

B

3

C

2

D

1

Answer

4

Explanation

Solution

Given equation lml \neq m

i.e., (lm)x25(l+m)x2(lm)=0(l - m)x^{2} - 5(l + m)x - 2(l - m) = 0 and x28x+(a26a)=0x^{2} - 8x + (a^{2} - 6a) = 0

2<a<8- 2 < a < 8 and 2<a<82 < a < 8

2a8- 2 \leq a \leq 8 and 2a82 \leq a \leq 8

x2+23x+3=0x^{2} + 2\sqrt{3}x + 3 = 0 and (cosp1)x2+(cosp)x+sinp=0(\cos p - 1)x^{2} + (\cos p)x + \sin p = 0.

i.e., Four solutions of this equation.