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Quadratic Polynomial

What are the ...

Question

What are the minimum and maximum numbers of distinct real roots a quadratic equation can have?

A

0, 2

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B

0, 1

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C

1, 2

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D

1, 1

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Solution

The correct option is A
0, 2

For quadratic equation $a x^{2} + b x + c = 0$

If discriminant D = $b^{2} - 4 a c > 0$ , it has 2 distinct real roots.

If D < 0, quadratic equation has no real roots.

$∴$ Minimum real roots = 0

Maximum real roots = 2

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Similar questions

What are the minimum and maximum numbers of distinct real roots a quadratic equation can have?

Q. (1)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(i)

x^{2} - 3 x + 4 = 0

(2)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(ii)

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

(3)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(iii)

2 x^{2} - 6 x + \frac{9}{2} = 0

(4)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(iv)

3 x^{2} - 4 x + 1 = 0

(5)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(v)

(x + 4)^{2} - 8 x = 0

(6)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(vi)

(x - \sqrt{2})^{2} - 2 (x + 1) = 0

(7)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(vii)

\sqrt{2} x^{2} - \frac{3}{\sqrt{2}} x + \frac{1}{\sqrt{2}} = 0

(8)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(viii)

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State whether the following quadratic equation have two distinct real roots. Justify your answer
(ix)

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State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x)

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Q. For the quadratic equation

a x^{2} + b x - 4 = 0, a, b \in R

a > 0,

then which of the following is always true?

Q. What is the minimum number of terms and maximum number of terms can a quadratic equation have?

Q. If a and b are distinct real numbers, show that the quadratic equation

2 (a^{2} + b^{2}) x^{2} + 2 (a + b) x + 1 = 0

has no real roots.

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