Question
Find the quadratic polynomial whose zeros are 2 and -6. Verify the relation between the coeficients and the zeros of the polynomial.
✓
Answer
Let $\alpha =2$ and $\beta=-6$
Sum of the zeros $=(\alpha+\beta)$
$=2+(-6) =- 4$
Product of the zeros $=\alpha\beta$
$=2\times(-6) =- 12$
$\therefore$ Required polynomial $=\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta$
$=\text{x}^2-(-4)\text{x}-12$
$=\text{x}^2+\text{4x}-12$
Sum of the zeros = -4
$=\frac{-4}{1}=\frac{-(\text{Coefficient of x})}{(\text{Coefficient of }\text{x}^2)}$
Product of the zeros = -12
$=\frac{-12}{1}=\frac{\text{Constant term}}{\text{Coefficient of }\text{x}^2}$
Sum of the zeros $=(\alpha+\beta)$
$=2+(-6) =- 4$
Product of the zeros $=\alpha\beta$
$=2\times(-6) =- 12$
$\therefore$ Required polynomial $=\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta$
$=\text{x}^2-(-4)\text{x}-12$
$=\text{x}^2+\text{4x}-12$
Sum of the zeros = -4
$=\frac{-4}{1}=\frac{-(\text{Coefficient of x})}{(\text{Coefficient of }\text{x}^2)}$
Product of the zeros = -12
$=\frac{-12}{1}=\frac{\text{Constant term}}{\text{Coefficient of }\text{x}^2}$
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
Prove the following identities:
$\frac{\tan\theta}{(\sec\theta-1)}+\frac{\tan\theta}{(\sec\theta+1)}=2\text{cosec}\theta$
→$\frac{\tan\theta}{(\sec\theta-1)}+\frac{\tan\theta}{(\sec\theta+1)}=2\text{cosec}\theta$
In the following figure, shows the cross-section of railway tunnel. The radius OA of the circular part is 2m. If $\angle\text{AOB}=90^\circ,$ calculate
→- The height of the tunnel
- The perimeter of the cross-section
- The area of the cross-section.
A tent of a circus is such that its lower part is cylindrical and upper part is conical. The diameter of the base of the tent is $48 \mathrm{~m}$ and the height of the cylindrical part is $15 \mathrm{~m}$. Total height of the tent is $33 \mathrm{~m}$. Find area of canvas required to make the tent. Also find volume of air in the tent.
→Each coefficient in equation $a x^2+b x+c=0$ is obtained by throwing an ordinary die. Find the probability that the equation has real roots.
→A fish tank is in the form of a cuboid, external measures of that cuboid are 80 cm x 40 cm × 30 cm. The base, side faces and back face are to be covered with a coloured paper. Find the area of the paper needed.
Find the lengths of the medians AD and BE of $\triangle\text{ABC}$ whose vertices are A(7, -3), B(5, 3) and C(3, 1).
→A meeting hall has 20 seats in the first row, 20 seats in the second, 28 seats in the third row and so on and has in all 30 rows. How many seats are there in the meeting hall?
In the given figure, AB is a diameter of a circle with centre O and AT is a tangent. If $\angle\text{AOQ}=58^{\circ},$find $\angle\text{ATQ}.$
→If $\sec \theta=\frac{13}{12}$ find the values of other trigonometric ratios.
→Two A.P.’s are given 9, 7, 5, . . . and 24, 21, 18, . . . . If nth term of both the progressions are equal then find the value of n and nth term.