Question

Find the values of k for which each of the following quadratic equation has equal roots: x square + 4kx + (k square - k + 2) = 0

Answer 1

AnsWer :

1 / 4.

Correct QuestioN :

Find the values of k for which each of the following quadratic equation has equal roots x² + 4kx + k = 0

SolutioN :

We have, Quadratic Equation.

→ x² + 4kx + k = 0.

Compare With General Equation.

ax² + bx + c = 0.

Where as,

• a = 1.
• b = 4k
• c = k.

$\rule{90}2$

Now, We know.

→ D = b² - 4ac.

Where as,

• D Discriminate.

→ D = ( 4k )² - 4( 1 ) (k )

→ D = 16k² - 4k.

Condition given both root are equal.

→ D = 0.

According to Condition :

→ D = 16k² - 4k.

→ 0 = 16k² - 4k.

→ 16k² = 4k.

→ 16k = 4.

→ k = 1 / 4.

$\rule{90}2$

Therefore, the value of k is 1 / 4.

Answer 2

$\sf{\underline{\large{\underline{\orange{Question:-}}}}}$

Find the values of k for which each of the following quadratic equation has equal roots: x square + 4kx + (k square - k + 2) = 0

$\sf{\underline{\large{\underline{\orange{Given:-}}}}}$

• $\sf x^2+4kx+k^2-k+2=0$
• Given equation have equal roots.

$\sf{\underline{\large{\underline{\orange{To\:Find:-}}}}}$

• $\sf Value\:of\:<strong>K</strong>=?$

$\sf{\underline{\large{\underline{\orange{General\: equation:-}}}}}$

$\sf{\fbox{\blue{\underline{\orange{ax^2+bx+c=0}}}}}$

Now,

Comparing the given equation with general equation

We get,

• $\sf a=1\\\sf b= 4k\\\sf c=k$

Since,

$\sf{\underline{\fbox{\red{ D ( discriminate)= b^2-4ac}}}}$

By the Formula

$\sf→ D= (4k)^2-4(1)(k)\\\sf→ D= 16k^2-4k$

By the Question

Both roots are equal.

$\sf→ D= 16k^2-4k\\\sf→ 0= 16k^2-4k\\\sf→ 16k=4\\\sf→k=\frac{16}{4}\\\sf{\fbox{\orange{\underline{\red{K=1/4}}}}}$