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RD Chapter 2 Polynomials Ex VSAQS Solutions

Question - 31 : - If α, β are the zeros of a polynomial such that α + β = -6 and α β = -4, then write the polynomial. [CBSE 2010]

Answer - 31 : -


Question - 32 : - If α, β are the zeros of the polynomial 2y2 + 7y + 5, write the value of α + β + αβ. [CBSE 2010]

Answer - 32 : -


Question - 33 : - For what value of k, is 3 a zero of the polynomial 2x2 + x + k ? [CBSE 2010]

Answer - 33 : -

3 is a zero of f(x) = 2x2 +x + k
It will satisfy the polynomial
f(x) = 0 ⇒ f(3) =0
Now 2x2 + x + k = 0
=> 2 (3)2 + 3 + k = 0
=> 18 + 3 + k = 0
=> 21 + k = 0
=> k = -21

Question - 34 : - For what value of k, is -3 a zero of the polynomial x2 + 11x + k ? [CBSE 2010]

Answer - 34 : -

-3 is a zero of polynomial f(x) = x2 +11x + k
It will satisfy the polynomial
f (x) = 0 => f(-3) = 0
Now x2 + 11x + k = 0
=> (-3)2+ 11 x (-3) + k = 0
⇒ 9 – 33+ k = 0
⇒ -24 +k = 0
⇒ k = 24

Question - 35 : - For what value of k, is -2 a zero of the polynomial 3x2 + 4x + 2k ? [CBSE 2010]

Answer - 35 : -

-2 is a zero of the polynomial
f(x) = 3x2 + 4x + 2k
f(-2) = 0
=> 3 (-2)2 + 4 (-2) + 2k = 0
=> 12 – 8 + 2k = 0
=> 4 + 2k = 0
=> 2k = -4
=> k = -2

Question - 36 : - If a quadratic polynomial f(x) is factorizable into linear distinct factors, then what is the total number of real and distinct zeros of f (x) ?

Answer - 36 : -

In a quadratic polynomial f(x) its degree is 2 and it can befactorised in to two distinct linear factors.
f(x) has two distinct zeros

Question - 37 : - If a quadratic polynomiaI f(x) is a square of a linear polynomial, then its two zeros are coincident. (True / False)

Answer - 37 : -

In a quadratic polynomial f(x), it is the square of a linear polynomial It has two zeros which are equal i.e. coincident
It is true

Question - 38 : - If a quadratic polynomial f(x) is not factorizable into linear factors, then it has no real zero. (True / False)

Answer - 38 : - A quadratic polynomial f(x) is not factorised into linear factors It has no real zeros It is true

Question - 39 : - If f(x) is a polynomial such that f(a) f(b) < 0, then what is the number of zeros lying between a and b ?

Answer - 39 : -

f(x) is a polynomial such that f(a) f(b) < 0
At least one of its zeros will be between a and b

Question - 40 : - If graph of quadratic polynomial ax2 + bx + c cuts positive direction of y-axis, then what is the sign of c ?

Answer - 40 : -

The graph of quadratic polynomial ax2 +bx + c cuts positive direction of y-axis Then sign of constant term c will bealso positive.

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