NCERT Class 10 Math Chapter 2 Important Questions Answer - Polynomials

Class 10 Math Chapter 2 Important Question Answer

Q1. Find a quadratic polynomial, the sum and product of whose zeroes are -3 and 2 respectively. Most Important

Ans. Let the quadratic polynomial be ax² + bx + c, and its zeroes be 𝛂 and β.

We have

𝛂 + β = -3 = $\displaystyle \frac{{-b}}{a}$ ,

𝛂 β = 2 = $\displaystyle \frac{c}{a}$

If a = 1, then b = 3 and c = 2.

So, one quadratic polynomial which fits the given conditions is x² + 3x + 2.

Q2. Find the product of zeroes of quadratic polynomial x² + 7x + 10. Most Important

Ans. Comparing x² + 7x + 10 with ax² + bx + c, we get a = 1, b = 7, c = 10,

As we know, Product of roots = $\displaystyle \frac{c}{a}$

= $\displaystyle \frac{{10}}{1}$ = 10

Q3. Find a quadratic polynomial with the given number as the sum and product of its zeroes respectively are 5 and 3. Most Important

Ans. Let the quadratic polynomial be ax² + bx + c, and its zeroes be 𝛂 and β.

We have

𝛂 + β = 5 = $\displaystyle \frac{{-b}}{a}$ ,

𝛂 β = 3 = $\displaystyle \frac{c}{a}$

If a = 1, then b = -5 and c = 3.

So, one quadratic polynomial which fits the given conditions is x² – 5x + 3.

Q4. Find a quadratic polynomial whose zeros are -3 and 5. Most Important

Ans. Let the quadratic polynomial be ax² + bx + c, and its zeroes be 𝛂 and β.

We have

𝛂 + β = -3 = $\displaystyle \frac{{-b}}{a}$ ,

𝛂 β = 5 = $\displaystyle \frac{c}{a}$

If a = 1, then b = 3 and c = 5.

So, one quadratic polynomial which fits the given conditions is x² + 3x + 5.

Q5. Product of roots of the quadratic polynomial 6x² – 7x – 3 is ____________.

Ans. Comparing 6x² – 7x – 3 with ax² + bx + c, we get a = 6, b = -7, c = -3,

As we know, Product of roots = $\displaystyle \frac{c}{a}$

= $\displaystyle \frac{{-3}}{6}$ = $\displaystyle -\frac{1}{2}$

Q6. Sum of the roots of the quadratic polynomnial 7x² – 3x + 1 is __________.

Ans. Comparing 7x² – 3x + 1 with ax² + bx + c, we get a = 7, b = -3, c = 1,

As we know , Sum of roots = $\displaystyle \frac{{-b}}{a}$

= $\displaystyle \frac{{-(-3)}}{1}$ = 3

Q7. Find the sum of zeroes of quadratic polynomial x² – 2x – 8. Most Important

Ans. Comparing x² – 2x – 8 with ax² + bx + c, we get a = 1, b = -2, c = -8

As we know, sum of zeroes = $\displaystyle \frac{{-b}}{a}$

= $\displaystyle \frac{{-(-2)}}{1}$ = 2

Also Read	Class 10 Math NCERT Solution
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