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Nature of Roots

Write the dis...

Question

Write the discriminant of the following quadratic equations:

(i) 2x² − 5x + 3 = 0
(ii) x² + 2x + 4 = 0
(iii) (x − 1) (2x − 1) = 0
(iv) x² − 2x + k = 0, k ∈ R
(v) $\sqrt{3} x^{2} + 2 \sqrt{2} x - 2 \sqrt{3} = 0$
(vi) x² − x + 1 = 0

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Solution

We have to find the discriminant of the following quadratic equations

(i) We have been given,

Now we also know that for an equation, the discriminant is given by the following equation:

Now, according to the equation given to us, we have,, and.

Therefore, the discriminant is given as,

Therefore, the discriminant of the equation is.

(ii) We have been given,

Now we also know that for an equation, the discriminant is given by the following equation:

Now, according to the equation given to us, we have,, and.

Therefore, the discriminant is given as,

Therefore, the discriminant of the equation is.

(iii) We have been given,

Now, simplify the equation to be represented in the quadratic form, so we have

Now we also know that for an equation, the discriminant is given by the following equation:

Now, according to the equation given to us, we have,, and.

Therefore, the discriminant is given as,

Therefore, the discriminant of the equation is.

(iv) We have been given,

Now we also know that for an equation, the discriminant is given by the following equation:

Now, according to the equation given to us, we have,, and.

Therefore, the discriminant is given as,

Therefore, the discriminant of the equation is.

(v) We have been given,

Now we also know that for an equation, the discriminant is given by the following equation:

Now, according to the equation given to us, we have,, and.

Therefore, the discriminant is given as,

Therefore, the discriminant of the equation is.

(vi) We have been given,

Now we also know that for an equation, the discriminant is given by the following equation:

Now, according to the equation given to us, we have,, and.

Therefore, the discriminant is given as,

Therefore, the discriminant of the equation is.

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Similar questions

Write the discriminant of the following quadratic equations:
(i) $2 x^{2} - 5 x + 3 = 0$ (ii) $x^{2} + 2 x + 4 = 0$
(iii) $(x - 1) (2 x - 1) = 0$ (iv) $x^{2} - 2 x + k = 0, k ϵ R$
(v) $\sqrt{3} x^{2} + 2 \sqrt{2} x - 2 \sqrt{3} = 0$ (vi) $x^{2} - x + 1 = 0$

Q. Find the discriminant of each of the following equations:

(i)

2 x^{2} - 7 x + 6 = 0

3 x^{2} - 2 x + 8 = 0

2 x^{2} - 5 \sqrt{2} x + 4 = 0

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

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

1 - x = 2 x^{2}

2x2−7x+6=02x2−7x+6=0

Q. Find the values of a, b, c for following quadratic equations by comparing with standard form.

(i) x² + 2x + 1 = 0
(ii) 2x² – x + 3 = 0
(iii) x² – x – 3 = 0
(iv) x² + 5x – 4 = 0
(v) x² – 7x + 4 = 0
(vi) 4x² – 9x + 1 = 0

Q. Find the roots of the quadratic equations by using the quadratic formula in the following equation:
(i)

2 x^{2} - 3 x - 5 = 0

5 x^{2} + 13 x + 8 = 0

- 3 x^{2} + 5 x + 12 = 0

- x^{2} + 7 x - 10 = 0

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

x^{2} - 3 \sqrt{5} x + 10 = 0

\frac{1}{2} x^{2} - \sqrt{11} x + 1 = 0

Find the nature of the roots of the following quadratic equations:
(i) $2 x^{2} - 8 x + 5 = 0$

(ii) $3 x^{2} - 2 \sqrt{6} x + 2 = 0$
(iii) $5 x^{2} - 4 x + 1 = 0$

(iv) $5 x (x - 2) + 6 = 0$
(v) $12 x^{2} - 4 \sqrt{15} x + 5 = 0$

(vi) $x^{2} - x + 2 = 0$

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