Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 131

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Which of the following graph represents the expression $f (x) = a x^{2} + b x + c (a \neq 0)$ , when $a > 0, b < 0$ and $c < 0$ ?

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Important Questions on Quadratic Equations

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 132

The expression

y = a x^{2} + b x + c

has always the same sign as of

a

if

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 133

The entire graph of the expression

y = x^{2} + k x - x + 9

is strictly above the

x

-axis if and only if

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 134

If

a, b \in R, a \neq 0

and the quadratic equation

a x^{2} - b x + 1 = 0

has imaginary roots then

a + b + 1

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 135

If

a

and

b

are the non-zero distinct roots of

x^{2} + a x + b = 0,

then the least value of

x^{2} + a x + b

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 136

If

y = - 2 x^{2} - 6 x + 9,

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 137

If

f (x) = x^{2} + 2 b x + 2 c^{2}

and

g (x) = - x^{2} - 2 c x + b^{2}

are such that

\min f (x) > \max g (x),

then the relation between

b

and

c,

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 138

If

b > a,

then the equation

(x - a) (x - b) - 1 = 0,

has

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Alpha Question Bank for Engineering: Mathematics>Chapter 4 - Quadratic Equations>Exercise-1>Q 139

If

α, β

are the roots of the quadratic equation

x^{2} - 2 p (x - 4) - 15 = 0,

then the set of values of

' p'

for which one root is less than

1

and the other root is greater than

2

is