Solve, using formula :x^2+x-(a+2)(a+1)=0 - Vidyadip

Question

Solve, using formula :$x^2+x-(a+2)(a+1)=0$

✓

Answer

Given quadratic equation is $x^2+x-(a+2)(a+1)=0$
Using quadratic formula,
$\Rightarrow x=\frac{-1 \pm \sqrt{1^2+4(a+2)(a+1)}}{2}$
$ \Rightarrow x=\frac{-1 \pm \sqrt{1+4\left(a^2+3 a+2\right)}}{2} $
$ \Rightarrow x=\frac{-1 \pm \sqrt{4 a^2+12 a+9}}{2} $
$ \Rightarrow x=\frac{-1 \pm \sqrt{2 a+3}^2}{2} $
$ \Rightarrow x=\frac{-1 \pm(2 a+3)}{2} $
$ \Rightarrow x=\frac{-1 \pm(2 a+3)}{2} \text { or } x=\frac{-1 \pm(2 a+3)}{2} $
$ \Rightarrow x=\frac{2 a+2}{2} \text { or } x=\frac{-2 a-4}{2}$
$\Rightarrow x=\frac{2(a+1)}{2} \text { or } x=\frac{2(-a-2)}{2} $
$\Rightarrow x = a +1 \text { or } x =- a -2=-( a +2)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[4 marks sum]" from Quadratic Equations→Quadratic Equations — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

A man bought 360 ten-rupee shares paying $12 \%$ per annum. He sold them when the price rose to Rs. 21 and invested the proceeds in five-rupee shares paying $4 \frac{1}{2} \%$ per annum at Rs. 3.5 per share. Find the annual change in his income.

A manufacturer sells a product to a trader A for Rs 15,000. Trader A sold it to trader B at a profit of Rs 2,000 and trader B sold it to trader C at a profit of Rs 1,500. Trader C made a profit of Rs 2,500 when he sold it to a customer. If VAT is calculated at 5%, find the amount of tax paid to the government. Also, find the price paid by the customer for the machine.

Prove that : $\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}=\sec A \cdot \operatorname{cosec} A+1$.

A manufacturer sells a microwave with a marked price of $Rs\ 11,000$ to the distributor for $Rs\ 7,500$. The distributor sells it to the retailer at a profit of $Rs\ 1,500$. The retailer sells to the customer at the marked price. If tax is charged at $8\%,$ find the $\text{VAT}$ paid by the retailer and the price paid by the customer.

If $x=\frac{\sqrt{a+1}+\sqrt{a-1}}{\sqrt{a+1}+\sqrt{a-1}}$ using properties of proportion show that $x^2-2 a x+1=0$

The angle of elevation of the top of a vertical cliff from a point 30 m away from the foot of the cliff is 60°. Find the height of the cliff.

As observed from the top of a $80\ m$ tall lighthouse, the angles of depression of two ships, on the same side of a light house in a horizontal line with its base, are $30^\circ$ and $40^\circ$ respectively. Find the distance between the two ships. Give your answer corrected to the nearest metre.

Prove the following trigonometric identities.$\frac{\cos A}{1-\tan A}+\frac{\sin A}{1-\cot A}=\sin A+\cos A$

Using the Remainder Theorem, factorise each of the following completely. $4x^3 + 7x^2 – 36x – 63$

A two digit number is such that the product of the digits is $12.$ When $36$ is added to this number the digits interchange their places. Determine the number.