Short-Answer Question: Write the zeros of the quadratic polynomia… - Vidyadip

Question

Short-Answer Question:
Write the zeros of the quadratic polynomial $\text{f}(\text{x})=4\sqrt3\text{x}^2+\text{5x}-2\sqrt3$

✓

Answer

We have,
$\text{f}(\text{x})=4\sqrt3\text{x}^2+\text{5x}-2\sqrt3$
$=4\sqrt3\text{x}^2+\text{8x}-\text{3x}-2\sqrt3$
$=\text{4x}\big(\sqrt3\text{x}+2\big)-\sqrt3\big(\sqrt3\text{x}+2\big)$
$=\big(\text{4x}-\sqrt3\big)\big(\sqrt3\text{x}+2\big)$
$\therefore\text{f}(\text{x})=0$
$\Rightarrow\big(\text{4x}-\sqrt3\big)\big(\sqrt3\text{x}+2\big)=0$
$\Rightarrow\text{4x}-\sqrt3=0$ or $\sqrt3\text{x}+2$
$\Rightarrow\text{x}=\frac{\sqrt3}{4}$ or $\text{x}=-\frac{2}{\sqrt3}$
So, the zeros of f(x) are $\frac{\sqrt3}{4}$ and $-\frac{2}{\sqrt3}$

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 "5 Marks Question" from Polynomials→Polynomials — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Draw a right triangle in which sides (other than hypotenuse) are of lengths 4cm and 3cm. Then, construct another triangle whose sides are $\frac53\text{times}$ the corresponding sides of the given triangle.

Draw a circle with the help of a bangle. Take any point P outside the circle. Construct the pair of tangents from the point P to the circle.

A hemispherical tank, full of water, is emptied by a pipe at the rate of $\frac{25}{7}$ litres per second. How much time will it take to empty half the tank if the diameter of the base of the tank is 3m?

If the mean of the following frequency distribution is 54, find the value of p.

Class	0-20	20-40	40-60	60-80	80-100
Frequency	7	p	10	9	13

Solve the following system of equations graphically:
3x + 2y = 12,
5x - 2y = 4

Prove that the angle between the two tangent drawn from an external point to a circle is supplenentary to the angle subtended by the line segments joining the points of contact at the centre.

Solve the following equations by using the method of completing the square:
$7x^2 + 3x - 4 = 0$

If two zeroes of the polynomial $p(x) = 2x^4 - 3x^3 - 3x^2 + 6x - 2 $are $\sqrt2$ and $-\sqrt2,$ find its other two zeroes.

Draw a $\triangle\text{ABC},$ right-angled at $B$ such that $AB = 3cm$ and $BC = 4cm.$ Now, Construct a triangle a triangle similar to $\triangle\text{ABC},$ each of whose sides is $\frac75\text{times}$ the correponding side of $\triangle\text{ABC}.$

Find the roots of the following equations, if they exist, by applying the quadratic formula:
$x^2 + 6x - (a^2 + 2a -8) = 0$