Determine the value of c for which the equation x2 -2cx + (7c-12)=0 has real and - Maths - Quadratic Equations

Question

Determine the value of c for which the equation x2
-2cx + (7c-12)=0 has real and equal roots

Lalit Mehra · Accepted Answer

Dear Student!

$T h e g i v e n q u a d r a t i c e q u a t i o n i s x^{2} - 2 c x + (7 c - 12) = 0$

Here, A = 1, B = – 2c and C = (7c – 12)

The given quadratic equation has real and equal roots, therefore, its discriminant D = 0.

D = B² – 4AC = 0

$\Rightarrow (- 2 c)^{2} - 4 \times 1 \times (7 c - 12) = 0 \Rightarrow 4 c^{2} - 28 c + 48 = 0 \Rightarrow 4 (c^{2} - 7 c + 12) = 0 \Rightarrow c^{2} - 7 c + 12 = 0 \Rightarrow c^{2} - 3 c - 4 c + 12 = 0 \Rightarrow c (c - 3) - 4 (c - 3) = 0 \Rightarrow (c - 3) (c - 4) = 0 \Rightarrow c - 3 = 0 o r c - 4 = 0 \Rightarrow c = 3 o r c = 4$

Thus, the value of c is 3 or 4.

Cheers!

10

Determine the value of c for which the equation x2 -2cx + (7c-12)=0 has real and equal roots.

Determine the value of c for which the equation x² -2cx + (7c-12)=0 has real and equal roots.