Question

For what value of k, the equation 2x² + kx + 2 = 0 has equal roots​

Answer 1

Answer:

the value of k is 4

Step-by-step explanation:

D=b square-4ac

0=k square-4×2×2

0=k square-16

16=k square

k=4

Answer 2

Answer:

Given equation,

→ 2x² + kx + 2 = 0

We have to find out the value of k such that the given equation has real and equal roots.

Concept:

• The discriminant of a quadratic equation tells us about the nature of roots.
• If the discriminant is greater than 0, roots are real and distinct.
• If the discriminant is equal to 0, roots are equal and real.
• If the discriminant is less than 0, roots are imaginary.
• So, here, we will find out the value of discriminant and form an equation and then on solving the equation, we will get the value of k.

The standard form of quadratic equation is -

→ ax² + bx + c = 0

Discriminant is calculated by using the formula given below,

→ D = b² - 4ac

In the given equation,

→ a = 2

→ b = k

→ c = 2

So, discriminant will be,

= k² - 4 × 2 × 2

= k² - 16

So, if the roots are real and equal, then D = 0,

→ k² - 16 = 0

→ k² = 16

→ k = √16

→ k = ±4

★ So, the possible values of k are 4 and -4 such that the roots of the given equation are real and equal.

Answer:

• k = 4, -4

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