Factorisation of Quadratic Polynomials
Trending Questions
Q.
Factorise:.
Q. Question 1 (ii)
For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.
iii) −2√3, −9
For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.
iii) −2√3, −9
Q.
The numerator of a fraction is 3 less than its denominator. If 1 is added to the denominator, the fraction is decreased by 115. Find the fraction.
Q. Solve the following quadratic equations by factorization method: [2 MARKS]
(i) x2−8x+16=0
(ii) x2+14x–32=0
(i) x2−8x+16=0
(ii) x2+14x–32=0
Q. If α and β are the zeroes of the quadratic polynomial 4x2+4x+1, then form a quadratic polynomial whose zeroes are 2α and 2β.
- x2+x+1
- x2−2x+1
- x2+2x+1
- x2+12x+1
Q. What are the factors of x2+5x−24?
- (x+3)(x+8)
- (x−3)(x−8)
- (x−3)(x+8)
- (x+3)(x−8)
Q. The zeroes of the following quadratic polynomial 6x2+x−5 are .
- 12 & 1
- 56 & -1
- -1 & 2
Q.
Determine which of the following polynomials has a factor :
Q.
Determine which of the following polynomials has a factor :
(ii)
Q. The zeroes of the following quadratic polynomial 6x2+x−5 are .
- 12 & 1
- 56 & -1
- -1 & 2
Q. If α and β are the zeroes of polynomial P(x)=x2−3x+2k, and α+β=α.β, then the value of k is ...............
- 3
- 1
- 3/2
- -3
Q. Question 1 (iv)
For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.
iv) =−32√5, −12
For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.
iv) =−32√5, −12
Q.
Which of the following is the factor of the polynomial
x3−3x2−10x+12 ?
x−0
x−1
x−2
x+1
Q. are the factors of the polynomial x2+2x−8.
- (x−4) & (x−2)
- (x+4) & (x−2)
- (x−4) & (x+2)
Q. Factorise the polynomial 2y3+y3−2y−1
- (y−1)(y−1)(2y+1)
- (y+1)(y+1)(2y+1)
- (y−1)(y+1)(2y+1)
- (y−1)(y−1)(2y−1)
Q. Question 1(i)
Find the roots of the following quadratic equations by factorisation:
(i) x2−3x−10=0
Find the roots of the following quadratic equations by factorisation:
(i) x2−3x−10=0
Q. If one of the zeroes of a quadratic polynomial (k−1)x2+kx+1 is -3, then the value of k is .
- 43
- −43
- 23
Q.
Let P(x)=4x2+9y2+16z2+12xy+24yz+16xz factorize P(x) for x=1, y=1, z=1.
- 81
- 36
- 64
- 49
Q.
Which of the following is a factor of (49x2−1)+(1+7x)2?
1−7x
1+7x
49x
x+1
Q. If one of the zeroes of a quadratic polynomial (k−1)x2+kx+1 is -3, then the value of k is .
- 43
- −43
- 23
Q.
Select the option that contains the factor of 4x3+4x2−x−1
(x+12)
(2x−1)
(x−3)
(2x−2)
Q. are the factors of the polynomial x2+2x−8.
- (x−4) & (x−2)
- (x+4) & (x−2)
- (x−4) & (x+2)
Q. Explain why 3.¯¯¯¯¯¯¯¯¯¯¯1416 is a rational number.
[1 mark]
[ <!--td {border: 1px solid #cccccc;}br {mso-data-placement:same-cell;}--> RS Aggarwal]
[Rational Numbers and Their Decimal Expansions]
[1 mark]
[ <!--td {border: 1px solid #cccccc;}br {mso-data-placement:same-cell;}--> RS Aggarwal]
[Rational Numbers and Their Decimal Expansions]
Q. Which among the following is a factor of x2+x6−16?
- 3x+1
- 2x+1
- x−15
- x−12
Q.
Factorise the given polynomial:
4a2−12ab+9b2+4a−6b- (2a−3b)(2a−3b+2)
- (2a+3b)(2a−3b+2)
- (2a−3b)(2a+3b−2)
- (2a+3b)(2a−3b−2)
Q.
Find the zeroes of the following quadratic polynomial 6x2+x−5.
12, 1
6, 5
56, −1
2, 1
Q. Solve the given quadratic equation by factorization method
x+3x−2−1−xx=174
x+3x−2−1−xx=174
Q. are the factors of the polynomial x2+2x−8.
- (x−4) & (x−2)
- (x+4) & (x−2)
- (x−4) & (x+2)
Q. are the factors of the polynomial x2+2x−8.
- (x−4) & (x−2)
- (x+4) & (x−2)
- (x−4) & (x+2)
Q. The zeroes of the following quadratic polynomial 6x2+x−5 are .
- 12 & 1
- 56 & -1
- -1 & 2