Question

For what value of k quadratic equation 4x^2+kx+1=0 has equal roots ​

Answer 1

Answer:

±4

Step-by-step explanation:

4k²+kx+1=0

For a quadratic equation,its root will be equal if its discriminant must be equal to zero.

So, Discriminant= D =k²-4.4.1= 0

(For ax² +bx+c=0, D= b²-4ac)

or, k²-16=0

or,k²=16

or,k= ±4

Answer 2

To Find :- For what value of k quadratic equation 4x^2+kx+1=0 has equal roots ?

Concept used :- If A•x^2 + B•x + C = 0, is any quadratic equation, then its discriminant is given by;

• D = B² - 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.

Solution :-

comparing given quadratic equation 4x^2+ kx + 1 = 0 with A•x^2 + B•x + C = 0 we get,

• A = 4
• B = k
• C = 1

since roots are equal , discriminant (D) is equal to zero .

then,

→ D = 0

→ B² - 4AC = 0

putting values,

→ (k)² - 4 × 4 × 1 = 0

→ k² - 16 = 0

→ k² = 16

Square root both sides,

→ k = √(16)

→ k = ± 4 (Ans.)

Hence, value of k is equal to 4 or (-4) .

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