Polynomials - MCQ Test - 1 - Class 9 MCQ

If α and β are the zeroes of a quadratic polynomial ax²+bx+c, then α+β = -b/a ∵ Sum of the zeroes of a quadratic polynomial ax²+bx+c = 

Let one zero be ααthen the other zero will be (−α)

A polynomial of degree 3 is called a cubic polynomial.

x²+9x+20 Splitting the middle term, we get
x²+5x+4x+20
= x(x+5)+4(x+5)
= (x+5)(x+4)
∴x+5 = 0 and x+4 = 0
⇒ x = −5 and x = −4

x²+5x−24
= x²+8x−3x−24
= x(x+8)−3(x+8) = (x+8)(x−3)
∴x+8 = 0 or x−3 = 0
⇒ x = −8 or x = 3

Given: p(x) = x³+7x²−2x−14 If √2 and –√2 are the two zeroes of p(x) then (x−√2) and (x+√2) and also (x−√2) (x+√2) = (x² - 2) is the factors of p(x).

Therefore, the third zero is x+7=0 ⇒ x = −7

A polynomial of degree 1 is called a linear polynomial.

Here,  

On comparing, we get a = 1,b = 4,c = 3 Putting these values in general form of quadratic polynomial ax²+bx+c we get x²+4x+3

x²−7x+12
= x²−4x−3x+12
= x(x−4)−3(x−4)
= (x−4)(x−3)
∴x−4 = 0 or x−3 = 0
⇒ x = 4or x = 3

The polynomial 9x²+6x+4 has no real zeroes because it is not factorizing.

Let α,β,γ are the zeroes of the given polynomial. ∴αβ = 2[Given] ∵ αβγ = -d/a

A polynomial of degree ‘n’ has at most ‘n’ zeroes because degree of a polynomial is equal to the zeroes of that polynomial only.

A real number ‘k’ is said to be a zero of a polynomial p(x), if p(k) is equals to 0.

If the zeroes of a quadratic polynomial ax²+bx+c, c ≠ 0 are equal, then c and a have the same sign always.

The number polynomials having zeroes as –2 and 5 is more than 3. If ‘S’ is the sum and ‘P’ is the product of the zeroes then the corresponding family of quadratic polynomial is given by p(x) = k(x²−Sx+P) where k is any real number. Therefore putting different values of k, we can make more than 3 numbers of polynomials.

If the polynomial 3x³−4x²−17x−k is exactly divisible by x−3, then

The degree of a constant polynomial is 0. e.g. 5 = 5 x 1 = 5×x⁰

If ‘α’, ‘β’ and ‘γ’ are the zeroes of a cubic polynomial ax³+bx²+cx+d, then α + β + γ = -b/a
∵ Sum of the zeroes of a cubic polynomial ax³+bx²+cx+d = 

If a real number ′α′ is a zero of a polynomial then (x−α) is a factor of that polynomial.

Let α,β,γ are the zeroes of the given polynomial. Given: α = 0 and To find : βγ Since,
 

The largest power of ‘x’ in p(x) is the degree of the polynomial.