Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 8

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IMPORTANT

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For a quadratic equation ${ax}^{2} + bx + c = 0$ , if you have equal roots and negative coefficient of $x^{2}$ , then the maximum value of $y$ is

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Important Questions on Theory of Equations

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IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 9

There are two quadratic equations; none of them has integer or complex roots. If each root of a quadratic equation is three times the root of another quadratic equation, then the maximum of this equation will be

m

times to that of the other equation. What's the value of

m

?

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Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 10

There are two quadratic equations

E_{1}

and

E_{2} .

Each root of

E_{1}

is four times to that of

E_{2}

, and the minimum of

E_{1}

will be

m

times to that of

E_{2}

. Then

m

is _____.

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Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 11

The two roots of a quadratic equation are

- 7

and

- 3

, what will be the maximum value of this equation?

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IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 12

Given the two certain roots of any quadratic equation, what is the locus of the vertices of all such quadratic graphs?

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IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 13

What is the locus of the vertices of all the quadratic equations whose roots are

m

times the certain given roots, say

α

and

β

?

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 14

The factors of a quadratic equation are

(x - 4)

and

(x - 8)

, what will be the vertex of the quadratic graph?

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Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 15

For a quadratic equation, the roots are $(-1,3)$ and the minimum is 4 units, then the triangle formed by connecting the roots and the minimum value of $y$ is

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IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 14 - SNAP>CMAT>Q 16

For a quadratic equation, the roots are

(- 3, 3)

and the maximum of

y

is

3 \sqrt{3}

units, then the triangle formed by connecting the roots and the maximum value of

y

is