The graph of the quadratic polynomial ax 2- bx - c intersect x axis such that C - b 2-4 a- then the quadratic polynomial has-A- Two distinct zeroesB- Two coincident zeroesC- No real zeroesD- None of the above

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Quadratic Equations

The graph of ...

Question

The graph of the quadratic polynomial $a x^{2} + b x + c$ intersect x axis such that $c = \frac{b^{2}}{4 a}$ , then the quadratic polynomial has,

Two distinct zeroes

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Two coincident zeroes

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No real zeroes

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None of the above

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Solution

The correct option is B Two coincident zeroes
Discriminant of $a x^{2} + b x + c$
$D = b^{2} - 4 a c$
When D = 0 ( two zeroes coincident)
$0 = b^{2} - 4 a c$
$b^{2} = 4 a c$
$c = \frac{b^{2}}{4 a}$ .

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The graph of the quadratic polynomial ax2+bx+c intersect x axis such that c=b24a, then the quadratic polynomial has,

The correct option is B Two coincident zeroesDiscriminant of ax2+bx+c D=b2−4ac When D = 0 ( two zeroes coincident) 0=b2−4ac b2=4ac c=b24a.

The graph of the quadratic polynomial $a x^{2} + b x + c$ intersect x axis such that $c = \frac{b^{2}}{4 a}$ , then the quadratic polynomial has,

The correct option is B Two coincident zeroes
Discriminant of $a x^{2} + b x + c$
$D = b^{2} - 4 a c$
When D = 0 ( two zeroes coincident)
$0 = b^{2} - 4 a c$
$b^{2} = 4 a c$
$c = \frac{b^{2}}{4 a}$ .