Question

If a, b, c ER and equations ax2 + bx + c = 0
and x2 + 4x + 5 = 0 have a common root
then
Question Type: Multiple Correct Type
1 a + b + c = 9
2 a + b × c = 25
a + b
3
1
4 b2 + 4 = 4ac​

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Asked on December 26, 2019 by

Shree D'Souza

If the equations x

2

+4x+5=0 and ax

2

+bx+c=0 have a common root (where a,b,c∈N), then the least value of a+b+c is equal to:

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ANSWER

The root of the given equation x

2

+4x+5=0 are

x=

2

−4±

16−20

=−2±i, where i=

−1

.

Now, for the equation ax

2

+bx+c=0, where a,b,c are positive integers, has a common root with the first equation.

As the two roots of the first equation are complex and a,b,c are natural numbers, the second equation also will have the same roots.

As complex roots occurs in pairs of a quadratic equation with real co-efficient.

For least value of a,b,c we will get least a+b+c

For that case the second equation will be same as the first

So, a+b+c=1+4+5=10.