# What is the value of m in 4x^2+44x+m=0 so that the 2 roots are equal?show steps please

neela | High School Teacher | (Level 3) Valedictorian

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4x^2+44x+m =0

To find the value m such that the two roots are equal.

We know that whem the two roots are equal , the left side expression 4x^2+44x+m should be a perfect square.

Therefore 4x^2+44x+m = (X+Y)^2  = X^2+2XY +Y^2.

Therefore identifying both sides term by term,

X^2 = 4x^2 . So X = 2x.

Y^2 = m . So  Y = sqrt(m)

2XY = 2(2x)*sqrtm = 44x

4x*sqrtm = 44x

sqrtm = 44x/4x =11

m = 11^2 = 121

So m = 121

william1941 | College Teacher | (Level 3) Valedictorian

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We are given the equation 4x^2+44x+m=0.

We'll use the relation that for an equation ax^2 + bx +c = 0

The roots are given by : [-b +sqrt(b^2-4ac)] / 2a and [-b - sqrt(b^2-4ac)]

Now as the roots are equal it implies that sqrt(b^2-4ac) = 0

we have a = 4 , b = 44 and c =m

substituting we get

sqrt [ 44^2 - 4*4*m] =0

=> 44^2 - 4*4*m =0

=> 44^2 = 16 m

=> m = 44^2 / 16

=> m = 121

Therefore the value of m for the equation having equal roots is 121.

[ We can see that the root of the equation 4x^2 + 44x + 121 =0 is only -5.5 ]