Question

Q.4 Find m , if quadratic equation (m-
12)x2 +2(m-12)x+2=0 has real and
equal roots.​

Answer 1

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Step-by-step explanation:

Q.4 Find m , if quadratic equation (m-

12)x2 +2(m-12)x+2=0 has real and

equal roots.​

⇒Given:

(α-12) x2 +2(α-12)x +2 = 0

Here

a = (α-12) ; b = 2(α-12) ; c = 2

It is given that the roots of the equation are equal; therefore we have

D = 0

⇒ ( b² -4ac ) = 0

⇒ {2(m-12)}² - 4×(m-12)×2 = 0

⇒ 4(m²-2m+144) - 8m + 96 = 0

⇒ 4m² - 96m +576 - 8m  + 96 = 0

⇒ 4m² - 104m + 672 = 0

⇒ m² - 26m + 168 = 0

⇒ m² - 14m - 12m + 168 = 0

⇒ m(m-14) -12(m-14) = 0

⇒ (m-14) (m-12) = 0

∴ m = 14 or m = 12

∵If the value of m is 12 then the equation becomes non-quadratic.

∴ the value of m will be 14 for the equation to have equal roots.