Question
Determine whether the given quadratic equations have equal roots and if so, find the roots:
$x^2+ 2x + 4 = 0$
$x^2+ 2x + 4 = 0$
✓
Answer
The given quadratic equation is
$x^2+ 2x + 4 = 0$
Here, $a = 1, b = 2$ and $c = 4$
Descriminant
$= b^2 - 4ac$
$= (2)^2 - 4 x 1 x 4$
$= 4 - 16$
$= -12 < 0$
Hence, the given equation has no real roots.
$x^2+ 2x + 4 = 0$
Here, $a = 1, b = 2$ and $c = 4$
Descriminant
$= b^2 - 4ac$
$= (2)^2 - 4 x 1 x 4$
$= 4 - 16$
$= -12 < 0$
Hence, the given equation has no real roots.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Given that $\tan \left(\theta_1+\theta_2\right)$ Given that $\tan \left(\theta_1+\theta_2\right)$ $=\frac{\tan \theta_1+\tan \theta_2}{1-\tan \theta_1 \tan \theta_2}$ Find $(\theta _1 + \theta _2)$ when $\tan \theta _1 = \frac{1}{2}$ and $\tan \theta_2=\frac{1}{3}$.
→Solve the following equation by factorization$\frac{1}{7}(3 x-5)^2=28$
→Mrs. Kapoor opened a Savings Bank Account in State Bank of India on 9th January 2008. Her passbook entries for the year 2008 are given below:
Mrs. Kapoor closes the account on 31st December, 2008. If the bank pays interest at 4% per annum, find the interest Mrs. Kapoor receives on closing the account. Give your answer correct to the nearest rupee.
| Date | Particulars | Withdrawals (in ₹) |
Deposits (in ₹) |
Balance (in ₹) |
| Jan. 9, 2008 | By cash | - | 10,000 | 10,000 |
| Feb. 12, 2008 | By cash | - | 15,500 | 25,500 |
| April 6, 2008 | To Cheque | 3,500 | - | 22,000 |
| April 30, 2008 | To Self | 2,000 | - | 20,000 |
| July 16, 2008 | By Cheque | - | 6,500 | 26,500 |
| August 4, 2008 | To Self | 5,500 | - | 21,000 |
| August 20, 2008 | To Cheque | 1,200 | - | 19,800 |
| Dec. 12, 2008 | By Cash | - | 1,700 | 21,500 |
Mrs. Kapoor closes the account on 31st December, 2008. If the bank pays interest at 4% per annum, find the interest Mrs. Kapoor receives on closing the account. Give your answer correct to the nearest rupee.
Prove.
$\frac{\cos A}{1-\tan A}+\frac{\sin A}{1-\cot A}=\sin A+\cos A$
→$\frac{\cos A}{1-\tan A}+\frac{\sin A}{1-\cot A}=\sin A+\cos A$
The sides of a right-angled triangle are $(x – 1)\ cm, 3x\ cm$ and $(3x + 1)\ cm.$ Find:(1) the value of $x,$
(2) the lengths of its sides,
(3) its area.
→(2) the lengths of its sides,
(3) its area.
Calculate the area of the shaded region, if the diameter of the semi-circle is equal to 14 cm. (Take π = 22/7).
Two dice are rolled together. Find the probability of getting: a multiple of 2 on one die and an odd number on the other die.
Solve the inequation:
3z – 5 ≤ z + 3 < 5z – 9, z ∈ R.
Graph the solution set on the number line
3z – 5 ≤ z + 3 < 5z – 9, z ∈ R.
Graph the solution set on the number line
What least number must be added to each of the numbers $6, 15, 20$ and $43$ to make them proportional?
→Prove the following identity:
$
\frac{\sec A-1}{\sec A+1}=\frac{\sin ^2 A}{(1+\cos A)^2}
$
→$
\frac{\sec A-1}{\sec A+1}=\frac{\sin ^2 A}{(1+\cos A)^2}
$