Question

The value of k for which the quadratic equation 2x 2 -k x + k=0 has equal roots is

Answer 1

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• we need to find the value of k

$\huge\bf\underline \red{ \mathcal{S}olution:-}$

$\bf\underline{\purple{Given:-}}$

When roots are real and equal then Discriminant is equal to 0.

• D = 0

For a quadratic equation ax² + bx + c , expression b² - 4ac is called Discriminant.

• ★ Quadratic Equation :- 2x² - kx + k

here,

• a = 2
• b = - k
• c = k

⇛ b² - 4ac = 0

⇛ (-k)² - 4 × 2 × k = 0

⇛ k² - 8k = 0

⇛ k² = 8k

• Dividing both sides by k.

⇛ k²/k = 8k/k

⇛ k = 8

Hence,

• Value of k is 8

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Answer 2

Question :-

The value of k for which the quadratic equation 2x 2 -k x + k=0 has equal roots is.

Solution :-

• Quadratic equation ↓
• $\rm 2x^2 - k +k = 0$

Condition :-

• When root of any equation are equal then
• Discriminant ( D ) = 0

In the given equation,

• a = 2
• b = -k
• c = k

We know:-

$\rm \: Discriminant \: (D)= b^2 - 4ac = 0$

$\sf → D = (-k )^2 - 4 × 2 × k = 0$

$\sf → k^2 - 8k = 0$

$\sf→ k^2 = 8k$

$\sf → \frac{k^2}{k} = 8$

$\sf → k = 8$

Hence :-

• K = 8