Question
Write a quadratic polynomial, sum of whose zeros is $2\sqrt{3}$ and their product is $2$.
✓
Answer
Sum of zeros $=2\sqrt{3}$
and product of zeros $= 2$
Quadratic polynomial will be $f(x) = x^2$ - (sum of zeros) x + product of zeros
$ = \text{x}^2 – 2\sqrt{3}\text{x} + 2$
and product of zeros $= 2$
Quadratic polynomial will be $f(x) = x^2$ - (sum of zeros) x + product of zeros
$ = \text{x}^2 – 2\sqrt{3}\text{x} + 2$
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
For a certain distribution, mode and median were found to be 1000 and 1250 respectively. Find mean for this distribution using an empirical relation.
In a family of 3 children, find the probability of having at least one boy.
State the pair of triangles in the figure below are similar. Write the similarity criterion used by you for answering the question and also write the pair of similar triangles in the symbolic form:
Show that the system of equations $-x + 2y + 2 = 0$ and $\frac{1}{2}\text{x}-\frac{1}{4}\text{y}-1=0$ has a unique solution.
→Define $HCF$ of two positive integers and find the $HCF$ of the following pairs of numbers:
$75$ and $243$
→$75$ and $243$
Find the point$(s)$ on the $x-$axis which is at a distance of $\sqrt{41}$ units from the point $(8,-5)$.
→If two tangents inclined at an angle of $60^{\circ}$ are drawn to a circle of radius $3 \ cm ,$ then find the length of each tangent.
→In a circle of radius 10 cm, an arc subtends an angle of 108° at the centre. what is the area of the sector in terms of $\pi$ ?
→A rational number in it's decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form $\frac{\text{p}}{\text{q}}$? Give reasons.
→Find:
$10^{th}$ term of the $A.P. 1, 4, 7, 10, .....$
→$10^{th}$ term of the $A.P. 1, 4, 7, 10, .....$