Question

If zeros of quadratic polynomial of x^2-(k+2)x+(k+1) are equal then the value of k is?

Answer 1

Gɪᴠᴇɴ :-

• zeros of quadratic polynomial of x^2-(k+2)x+(k+1) are equal...

Tᴏ Fɪɴᴅ :-

• Value of k ?

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

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...

Sᴏʟᴜᴛɪᴏɴ :-

Comparing The Given Polynomial x^2-(k+2)x+(k+1) = 0 with A•x^2 + B•x + C = 0 we get :-

➼ A = 1

➼ B = - (k + 2)

➼ C = (k + 1)

Now, we Have given That, Zeros of the Given Polynomial are Equal.

Therefore,

➼ D = B^2 - 4•A•C = 0

➼ [-(k + 2)]² - 4 * 1 * (k + 1) = 0

➼ [ (k + 2)² ] - 4(k + 1) = 0

➼ [ k² + 4k + 4 ] - 4k - 4 = 0

➼ k² + 4k + 4 - 4k - 4 = 0

➼ k² + (4k - 4k) + (4 - 4) = 0

➼ k² + 0 + 0 = 0

➼ k² = 0

➼ k = 0

Hence, value of k will be 0(Zero).