Download App

Polynomials — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsPolynomials5 Marks
Question
Find the quadratic polynomial whose zeros are $\frac{2}{3}$ and $\frac{-1}{4}.$ Verify the relation between the coefficients and the zeros of the polynomial.
✓

Answer

Let $\alpha$ and $\beta$ are the zeros then
$\alpha +\beta=\frac{2}{3}+\Big(-\frac{1}{4}\Big)$
$=\frac{8-3}{12}=\frac{5}{12}$
$\alpha\beta=\frac{2}{3}\times\Big(-\frac{1}{4}\Big)$
$=-\frac{2}{12}=-\frac{1}{6}$
$\therefore$ quadratic polynomial whose zeros are $\alpha,\beta$ is:
$\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta$
$=\text{x}^2-\Big(\frac{5}{12}\Big)\text{x}+\Big(-\frac{1}{6}\Big)$
$=\frac{1}{12}(\text{12x}^2-\text{5x}-2)$
Sum of zeros $=-\frac{\text{Coefficient of x}}{\text{Coefficients of }\text{x}^2}$
$=-\frac{-5}{12}=\frac{5}{12}$
Also sum of zeros $=\frac{2}{3}+\Big(-\frac{1}{4}\Big)$
$=\frac{5}{12}$
Product of zeros $=\frac{\text{Constant term}}{\text{Coefficient of }\text{x}^2}$
$=\frac{-2}{12}=\frac{-1}{6}$
Also product of zeros $=\frac{2}{3}\times\Big(-\frac{1}{4}\Big)$
$=\frac{-2}{12}=\frac{-1}{6}$

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 line segment of length $7.6\ cm$ and divide it in the ratio $5 : 8$. Measure the two parts.
→
Solve each of the following given systems of equations graphically and find the vertices and area of the triangle formed by these lines and the x-axis:
2x - 3y + 4 = 0, x + 2y - 5 = 0
→
Solve the following quadratic equation:
$4^{(x+1)} + 4^{(1-x)} = 10$
→
If 1 is added to both of the numerator and denominator of a fraction, it becomes $\frac{4}{5}.$ If however, 5 is subtracted from both numerator and denominator, the fraction $\frac{1}{2}.$ Find the fraction.
→
Find the roots of the following equation, if they exist, by applying the quadratic formula:
$x^2 + 5x - (a^2 + a - 6) = 0$
→
Each of the equal sides of an isosceles triangle measures 2cm more than its height, and the base of the triangle measures 12cm. Find the area of the triangle.
→
A bucket is in the form of a frustum of a cone with a capacity of $12308.8\ cm^3 $ of water. The radii of the top and bottom circular ends are $20\ cm$ and $12\ cm$, respectively. Find the height of the bucket. $[$Use $\pi = 3.14]$
→
If 45 is subtracted from twice the greater of two numbers, it result in the other number. If 21 is subtracted from twice the smaller number, it results in the greater number. Find the numbers.
→
A jeweller has bars of 18-carat gold and 12-carat gold. How much of each must be melted together to obtain a bar of 16-carat gold, weighing 120 g? (Given: Pure gold is 24-carat).
→
Two years ago, a man was five times as old as his son. Two years later, his age will be 8 more than three times the ago of the son. Find their present ages.
→