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Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : (2  √3) is one zero of the quadratic polynomial then other zero will be (2 + √3)
Reason : Irrational zeros (roots) always occurs in
Thus (a) is correct option.
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : The graph y = f(x) is shown in figure, for the polynomial f(x). The number of zeros of f(x) is 4.
Reason : The number of zero of the polynomial f(x). is the number of point of which f(x) cuts or touches the axes.
As the number zero of polynomial f(x) is the number of points at which f(x) cuts (intersects) the x axis and number of zero in the given figure is 4. So A is correct but R is incorrect.
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If p(x) ax + b, a ≠ 0 is a linear polynomial, then x = b/a is the only zero of p(x).
Reason : A linear polynomial has one and only one zero.
Because on Xaxis the value of yco ordinate is zero.
Given equation is y = ax + b
Now on substituting y = 0 we get ax + b = 0
⇒ ax = −b
⇒ x = b/a
Therefore the coordinates are ( b/a, 0).
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If one zero of polynominal p(x) = (k^{2} + 4) x^{2} + 13x + 4k is reciprocal of other,
then k = 2.
Reason : If (x  α) is a factor of p(x), then p(α) = 0 i.e. α is a zero of p(x).
K2  4k + 4 = 0
(k  2)^{2} = 0 ⇒ k = 2
Assertion is true Since, Reason is not correct for Assertion.
Thus (b) is correct option.
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : Degree of a zero polynomial is not defined.
Reason : Degree of a nonzero constant polynomial is ‘0’
The constant polynomial 0 is called a zero polynomial.
The degree of a zero polynomial is not defined.
∴ Assertion is true.
The degree of a nonzero constant polynomial is zero.
∴ Reason is true.
Since both Assertion and Reason are true and Reason is not a correct explanation of Assertion.
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : The degree of the polynomial (x  2) (x 3) (x + 4) is 4.
Reason : The number of zeroes of a polynomial is the degree of that polynomial.
= (x  2)[x^{2} + 4x  3x  12]
= (x  2)(x^{2} + x  12)
= x^{3} + x^{2}  12x  2x^{2}  2x + 24
p(x) = x^{3}  x^{2}  14x + 24
So, degree of p(x) h = 3
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : p(x) = 14x^{3}  2x^{2} + 8x^{4} + 7x  8 is a polynomial of degree 3.
Reason : The highest power of x in the polynomial p(x) is the degree of the polynomial.
Thus (d) is correct option.
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If both zeros of the quadratic polynomial x^{2}  2kx + 2 are equal in magnitude but opposite in sign then value of k is 1/2.
Reason : Sum of zeros of a quadratic polynomial ax^{2} + bx + c is b/a
⇒ 2k = 0 & k = 0
So, A is incorrect but R is correct.
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If f(x) = x^{4} + x^{3}  2x^{2} + x + 1 is divided by (x  1), then its remainder is 2.
Reason : If p(x) be a polynomial of degree greater than or equal to one, divided by the linear polynomial x  a , then the remainder is p(a).
Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : x^{3} + x has only one real zero.
Reason : A polynomial of n th degree must have n real zeroes.
Again, x^{3} + x = x(x^{2} + 1)
which has only one real zero because x^{2} + 1 ≠ 0 for all x ∈ R.
Assertion (A) is true but reason (R) is false.
Thus (c) is correct option.
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