Question

If the roots of the equations 3/4x² +9x+c³= 0 are equal then c is equal to
(a) 5
(b) 3
(c) 8
(d) 5​

Answer 1

Answer:

(c) 3

Step-by-step explanation:

Concept= Quadratic Equation

Given= The quadratic equation with both root equal

To find= The value of c

Explanation=

We have been the question as if the roots of the equations 3/4x² +9x+c³= 0 are equal then c is equal to

(a) 5

(b) 3

(c) 8

(d) 5​

So the quadratic equation is  3/4x² +9x+c³= 0

So we reduce the equation by multiplying it by 4 on both sides.

4* 3/4x² + 4*9x + 4*c³= 0*4

3x² + 36x + 4c³= 0  

So we have been the condition that both roots are equal.

When the given quadratic equation is ax² + bx + c =0

The Condition for equal roots is b² - 4ac =0 or b² = 4ac.

In this equation 3x² + 36x + 4c³= 0 the value of a= 3, b= 36  and c= c³

So the equation holds as : 36² = 4*3*c³

=> 39*36 = 4*3*c³

=> 9*9 = 3*c³

=> 27 = c³

=> c= 3

Therefore the value of c is 3.

Hence option (c) is correct.

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