Download App

Polynomials — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsPolynomials1 Mark
MCQ
A quadratic polynomial whose zeros are $\frac{3}{5}$ and $\frac{-1}{2}$ is :
  • A
    $ 10 x^2+x+3 $
  • B
    $ 10 x^2+x-3 $
  • C
    $ 10 x^2-x+3 $
  • ✓
    $ 10 x^2-x-3 $
✓

Answer

Correct option: D.
$ 10 x^2-x-3 $
Let $\alpha$ and $\beta$ be the zeros of the required quadratic polynomial.
Then, we have
$\alpha+\beta=\frac{3}{5}+\Big(-\frac{1}{2}\Big)$
$=\frac{6-5}{10}=\frac{1}{10}$
$\alpha\beta=\frac{3}{5}\times\Big(-\frac{1}{2}\Big)=-\frac{3}{10}$
Now, a quadratic polynomial whose zeros are $\alpha$ and $\beta$ is given by
$\text{p}(\text{x})=\text{x}^2-(\alpha+\beta)\text{x}+\alpha\beta$
$\Rightarrow\text{p}(\text{x})=\text{x}^2-\Big(\frac{1}{10}\Big)\text{x}+\Big(-\frac{3}{10}\Big)$
$=\text{x}^2-\frac{1}{10}\text{x}-\frac{3}{10}$ or $10\text{x}^2-\text{x}-3$

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 "M.C.Q (1 Marks)" from Polynomials→Polynomials — all question types→Maths STD 10 question papers→CBSE Board STD 10 question papers→CBSE Board question paper generator→

Similar questions

If the point $P ( k -1,2)$ is equidistant from the points $A (3, k )$ and $B ( k , 5)$, then the value of $k$ equal to.
→
The probability of getting an even number, when a die is thrown once, is:
→
If the sum of the roots of the equation $x^2-(k+6) x+2(2 k-1)=0$ is equal to half of their product, then $k =$
→
In a right triangle $\text{ABC},$ right angled at $B, BC = 12\ cm$ and $AB = 5\ cm$. The radius of the circle inscribed in the triangle is :
→
The circular ends of a bucket are of radii $35\ cm$ and $14\ cm$ and the height of the bucket is $40\ cm.$ Its volume is :
→
If the roots of the equations $(a^2+ b^2)x^2- 2b(a + c)x + (b^2+ c^2) = 0$ are equal, then :
→
The diameter of a circle whose area is equal to the sum of the areas of two circles of radii $12 \ cm$ and $5 \ cm$ is
→
The $\text{HCF}$ of $95$ and $152$, is :
→
If an arc of a circle of radius $14 \ cm$ subtends an angle of $60^\circ$ at the centre, then the length of the arc is $\frac{44}{3}\text{ cm}.$
→
If in two triangle ABC and DEF, $\angle\text{A}=\angle\text{E},\ \angle\text{B}=\angle\text{F},$ then which of the following is not true?
→