Arrange the following equations based on their discriminant value such that D>0 is on top & D<0 is at bottom.

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

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10 x^{2} + 6 x + 2 = 0

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x^{2} + 7 x + 1 = 0

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2 x^{2} + 5 x + 1 = 0

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Solution

Discriminant(D) is given by D = $b^{2} - 4 a c$

Let's find the 'D' for each of the given equations.

1. $x^{2} + 4 x + 4 = 0$

Using Discriminant formula, we have

D = $4^{2} - 4 (1) (4)$ = 16-16 = 0

2. $10 x^{2} + 6 x + 2 = 0$

Using Discriminant formula, we have

D= $6^{2} - 4 (10) (2)$ = 36-80 = -44

$\Rightarrow$ D<0

3. $x^{2} + 7 x + 1 = 0$

Using Discriminant formula, we have

D = $7^{2} - 4 (1) (1)$ = 49-4 = 45

$\Rightarrow$ D>0

4. $2 x^{2} + 5 x + 1 = 0$

Using Discriminant formula, we have

D = $5^{2} - 4 (2) (1)$ = 25-8 = 17

$\Rightarrow$ D>0

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Question 3
Which of the following equations has 2 as a root?
(a) $x^{2} - 4 x + 5 = 0$
(b) $x^{2} + 3 x - 12 = 0$
(c) $2 x^{2} - 7 x + 6 = 0$
(d) $3 x^{2} - 6 x - 2 = 0$

Question 3
Which of the following equations has 2 as a root?
(a) $x^{2} - 4 x + 5 = 0$
(b) $x^{2} + 3 x - 12 = 0$
(c) $2 x^{2} - 7 x + 6 = 0$
(d) $3 x^{2} - 6 x - 2 = 0$

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