If a,b,c are rational numbers and a+b+c=0;a,c>0. Now, consider the parabola represented by the quadratic expression y=ax2+bx+c. Then select the correct options.
A
x=1 is one of the roots of the equation
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B
If a=c⇒ vertex lies on x-axis
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C
Vertex lies in Ist quadrant
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D
Vertex lies in IVth quadrant
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Solution
The correct option is D Vertex lies in IVth quadrant Given : y=ax2+bx+c;a+b+c=0;a>0,c>0;a,b,c∈R
∵a+b+c=1⇒x=1 is one of the roots of the equation.
Product of roots =ca>0∵a,c>0. ∴ 2nd root of the equation will also be positive.
Thus the graph will look like this:
From the graph we can see that the vertex of the parabola lies on the IVth quadrant
Now, if the vertex lie on the x− axis then the y− coordinate of the vertex is equal to 0.