Question

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

Answer 1

Given :-

• Quadratic equation 5x²+kx-4 = 0

To Show:-

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

Solution:-

$\qquad$ ☀We are given quadratic equation is 5x²+kx-4 = 0

On comparing, we get :-

• a = 5
• b = k
• c = -4

$\qquad$ ☀We know that, If a quadratic equation ax²+bx+c = 0 has equal and real roots then the discriminant.

$\qquad\small\underline{\pmb{\sf \:According \: to \: the \: question :-}}$

$\blue{\qquad\leadsto\quad \pmb {\mathfrak{ D= b²-4ac = 0}}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ k²-4(5)(-4) = 0}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ k² -(-80) = 0}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ k² + 80 = 0}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ k² = -80}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ k = ±√-80}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ k = ±√(-1×80)}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ k =± √(80i²)}}$

$\blue{\qquad\leadsto\quad \pmb {\mathfrak{ k =±√80 i}}}$

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

$\qquad$ $\qquad$ Showed..!

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Answer 2

Answer:

Given equation

5x

2

−kx+4=0

Now for real roots b

2

−4ac≥0

Hence

k

2

−4(20)≥0

k

2

≥80

k≥4

5

or k≤−4

5

Explanation:

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