If the curve described by the equation y = x^2 + bx + c cuts the x-axi

Question

If the curve described by the equation  y = x^2 + bx + c  cuts the x-axis at -4 and y axis at 4, at which other point does it cut the x-axis?

A. -1
B. 4
C. 1
D. -4
E. 0

GMATWhizTeam · Answer

Solution:

We are given equation of a curve as  y = x^2 + bx + c .

We are given that this curve cuts the x-axis at  -4 . This means we can plug  x=-4  and  y=0  in the equation.

⇒ 0=(-4)^2-4b+c

⇒ c-4b=-16 ...... (i)

We are also given that this curve cuts the y-axis at  4 . This means we can plug  x=0  and  y=4  in the equation.

⇒ 4=0+0+c

⇒ c=4  .

We can plug this value of  c  in equation  i  to get the value of  b .

⇒ c-4b=-16

⇒ 4-4b=-16

⇒-4b=-20

⇒b=5

Now e can plug   c=4  ,   b=5   and   y=0   oin the equation of the curve to get the  x  intercepts:

⇒ x^2+bx+c=0

⇒ x^2+5x+4=0

⇒ x^2+4x+x+4=0

⇒ (x+4)(x+1)=0

So the value of  x  or  x-intercepts  can be  -1  and  -4 . We already know that one of  x-intercepts  is  -4 .

So, the other one is  -1 .

Hence the right answer is  Option A .

Foreheadson · Answer

Easy way. C=4. X1*X2=4. We know that X1=-4. so X2=4/-4=-1.

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