Question

5. Show that for no value of k, the equation 5x²+kx-4=0 has real and equal roots
of class 10 quadratic equation​

Answer 1

Step-by-step explanation:

Given :-

5x²+kx-4 = 0

To find:-

Show that for no real value of k, the equation 5x²+kx-4=0 has real and equal roots .

Solution:-

Given quadratic equation is 5x²+kx-4 = 0

On comparing this with the standard quadratic equation,

a = 5

b = k

c = -4

If a quadratic equation ax²+bx+c = 0 has equal and real roots then the discriminant

(D)= b²-4ac = 0

=> k²-4(5)(-4) = 0

=>k² -(-80) = 0

=> k² + 80 = 0

=> k² = -80

=>k = ±√-80

Therefore, k = √-80 or -√-80

k is not a real value

It is the imaginary numbers because

√-80 = √(-1×80)=√(80i²)=√80 i

Hence , Proved.

Answer:-

There is no real value of k ,the equation 5x²+kx-4 = 0 has real and equal roots.

Used formulae:-

If a quadratic equation ax²+bx+c = 0 has equal and real roots then the discriminant(D)=b²-4ac = 0

• i² = -1

Answer 2

Given equation

5x²−kx+4=0

Now for real roots b

2−4ac≥0

Hence

k²−4(20)≥0

k² ≥80

k ≥ 4√5 or k ≤ −4√5

Step-by-step explanation:

here is your answer mate! ❣️