If a -0 and D -0- what can be inferred about f x - ax 2- bx - c -A- f x is always negativeB- f x - is always positiveC- f x -0 alwaysD- cannot determine nature of f x

The correct option is A f(x) is always negative When a lt; 0,the graph of f(x) = ax^2+bx+c will be in the shape of inverted bowl. Also D lt; 0 indicates ...

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Standard XII

Mathematics

Discriminant

If a <0 and D...

Question

If a < 0 and D < 0, what can be inferred about $f (x)$ = $a x^{2} + b x + c$ ?

f(x) = is always positive

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f(x) is always negative

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f(x) = 0 always

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cannot determine nature of f(x)

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Solution

The correct option is B
f(x) is always negative

When a < 0,the graph of f(x) = $a x^{2} + b x + c$ will be in the shape of inverted bowl.

Also D < 0 indicates that f(x) does not cut x-axis

So, the graph of f(x) will look as

From graph, we can see that f(x) is always negative

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If a < 0 and D < 0, what can be inferred about $f (x)$ = $a x^{2} + b x + c$ ?

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If a < 0 and D < 0, what can be inferred about f(x) = ax2+bx+c?

The correct option is B f(x) is always negative When a < 0,the graph of f(x) = ax2+bx+c will be in the shape of inverted bowl. Also D < 0 indicates that f(x) does not cut x-axis So, the graph of f(x) will look as From graph, we can see that f(x) is always negative

If a < 0 and D < 0, what can be inferred about $f (x)$ = $a x^{2} + b x + c$ ?

The correct option is B
f(x) is always negative

When a < 0,the graph of f(x) = $a x^{2} + b x + c$ will be in the shape of inverted bowl.

Also D < 0 indicates that f(x) does not cut x-axis

So, the graph of f(x) will look as

From graph, we can see that f(x) is always negative