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If the curve described by the equation y = x2 + bx + c cuts the x-axis

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If the curve described by the equation y = x2 + bx + c cuts the x-axis  [#permalink]

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New post 10 Aug 2018, 10:08
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Difficulty:

  65% (hard)

Question Stats:

44% (01:53) correct 56% (02:01) wrong based on 36 sessions

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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

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Re: If the curve described by the equation y = x2 + bx + c cuts the x-axis  [#permalink]

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New post 10 Aug 2018, 10:49
+1 for A? I plugged in the other points to come up with an equation...not sure if I went about it the right way
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If the curve described by the equation y = x2 + bx + c cuts the x-axis  [#permalink]

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New post 10 Aug 2018, 22:08
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SajjadAhmad wrote:
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


Given, \(y = x^2 + bx + c\), cuts the x-axis at two points. One intersection point with x-axis is given. We need to find out the other point of intersection. In other words, 1 root of the quadratic equation is given, what is the value if the other root?

a) At (-4,0), \(0=(-4)^2+b*(-4)+c\) Or, 4b-c=16
b) At (0,4), \(4=0^2+b*0+c\) Or, c=4
So, 4b-4=16 Or, b=5.
Now, we have the equation of the curve, \(y=x^2+5x+4\), which has the roots: -4 and -1.
So, other other root is -1.

Ans. (A)
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If the curve described by the equation y = x2 + bx + c cuts the x-axis &nbs [#permalink] 10 Aug 2018, 22:08
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