The quadratic equation 2x2- -5x - 1 - 0 has

The correct option is D no real rootsDiscriminant =b^2 4ac=(√(5))^2 4(2)(1)=5 8= 3 lt;0 So, the equation has no real roots ...

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Standard X

Mathematics

Nature of Roots

The quadratic...

Question

The quadratic equation $2 x^{2} + \sqrt{5} x + 1 = 0$ has

two distinct real roots

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two equal real roots

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no real roots

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more than 2 real roots

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Solution

The correct option is D no real roots
Discriminant $= b^{2} - 4 a c = (\sqrt{5})^{2} - 4 (2) (1) = 5 - 8 = - 3 < 0$
So, the equation has no real roots

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Similar questions

Question 8
The quadratic equation $2 x^{2} - \sqrt{5} x + 1 = 0$ has
(A) two distinct real roots
(B) two equal real roots
(C) no real roots
(D) more than 2 real roots

Find the discriminant of the quadratic equation $3 x^{2} - 5 x + 2 = 0$ and find the nature of their roots.

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)

x (1 - x) - 2 = 0

(9)
State whether the following quadratic equation have two distinct real roots. Justify your answer
(ix)

(x - 1) (x + 2) + 2 = 0

(10)
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x)

(x + 1) (x - 2) + x = 0

Q. The given quadratic equations have real roots and roots are Real and equal,

\sqrt{\frac{3}{2}}

2 x^{2} - 2 \sqrt{6 x} + 3 = 0

Prove that the roots of the following quadratic equation has two real distinct roots.

2 x^{2} - 6 x + 3 = 0

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The quadratic equation 2x2+√5x+1=0 has

The correct option is D no real rootsDiscriminant=b2−4ac=(√5)2−4(2)(1)=5−8=−3<0So, the equation has no real roots

The quadratic equation $2 x^{2} + \sqrt{5} x + 1 = 0$ has

The correct option is D no real roots
Discriminant $= b^{2} - 4 a c = (\sqrt{5})^{2} - 4 (2) (1) = 5 - 8 = - 3 < 0$
So, the equation has no real roots