Question

find the value of a such that the quadratic equation(a-12xsquare +2(a-1)x+2=0 has equal roots​

Answer 1

Correct Question

Find the value of a such that the quadratic equation

(a - 12)x² + 2(a - 12)x + 2 = 0

has equal roots

Given

a quadratic equation (a - 12)x² + 2(a - 12)x + 2 = 0

To find

The value of a for which the equation has equal roots.

$\rule{200}2$

Answer

14

Solution

For having equal roots, discriminant of the quadratic equation should be equal to zero.

Discriminant = b² - 4ac

where, b is the coefficient of x, a is the coefficient of x² and c is the constant term.

Therefore,

[2(a - 12)]² - 4(a - 12)(2) = 0

→ 2²(a - 12)² = 8(a - 12)

→ 4(a - 12)² = 8(a - 12)

→ (a - 12)²/(a - 12) = 8/4

→ (a - 12) = 2

→ a = 12 + 2

→ a = 14.

Answer 2

Question :----

• find the value of a such that the quadratic equation(a-12)x² +2(a-1)x+2=0 has equal roots...

Points to Remember :------

If A•x^2 + B•x + C = 0 ,is any quadratic equation,

then its discriminant is given by;

D = B^2 - 4•A•C

• If D = 0 , then the given quadratic equation has real and equal roots.

• If D > 0 , then the given quadratic equation has real and distinct roots.

• If D < 0 , then the given quadratic equation has unreal (imaginary) roots.

_________________________________

in Equation Given (a-12)x² +2(a-1)x+2=0 , we have

• a = (a-12)
• b = 2(a-1)
• c = 2

since Roots Are Equal ,

Hence,

$\red{ \boxed{\sf{b}^{2} - 4ac = 0}}$

putting values we get,

→ [2(a-1)]² - 4(a-12)×2 = 0

→ 4(a-1)² - 8a + 96 = 0

→ 4a² + 4 - 8a - 8a + 96 = 0

→ 4a² -16a +100 = 0

→ 4(a² - 4a +25) = 0

→ a² - 4a + 25 = 0

Now, by brahmacharya formula ,,

$\green{\bf \: a \: = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} }$

Putting values we get,

$a_1 \: = \frac{4 + \sqrt{16 - 100} }{2} = 2 + \sqrt{( - 21)} \\ \\ a_2 = \frac{4 - \sqrt{16 - 100} }{2} = 2 - \sqrt{( - 21)}$

Hence, value of a will be 2±√(-21) if roots are Equal....

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