Q1. If one zero of the quadratic polynomial x2-5x-6 is 6, then find the other zero.
Q2. If both the zeroes of the quadratic polynomial ax2 + bx + c are equal and opposite in sign, then
find the value of 'b'?
Q3. Can x2 – 1 be the quotient on division of x6 + 2x3 + x – 1 by a polynomial in x of degree 5?
Q4. If 1 is a zero of the polynomial p(x) = ax2 - 3(a-1)x - 1, then find the value of 'a' ?
Q5. If on division of a polynomial p(x) by a polynomial g(x) the quotient is zero, what is the relation
between degree of p(x) and g(x)?
Q6. If one root of the polynomial p(y) = 5y2 +13y + m is reciprocal of other, then find the value of
‘m’? Q7. If the graph of a polynomial intersects the x – axis at only one point, can it be a quadratic
polynomial?
SHORT ANSWER TYPE QUESTIONS
Q8. What number should be added to the polynomial x2 -5x+4, so that 3 is the zero of the
polynomial? Q9. If α and β are zeros of p(x) = x2 +x-1, then find 1/α+ 1/β?
Q10. If α and β are the zeros of the quadratic polynomial f(x) = 2x2 -5x + 7, find a polynomial whose
zeros are 2α+ 3β and 3α+ 2β?
Q11. If one of the zeros of the cubic polynomial x3 + ax2 + bx + c is -1, then what will be the product
of the other two zeros?
Q12. What must be subtracted from p(x) = 8x4 + 14x3 - 2x2 +7x -8,so that the resulting polynomial is
exactly divisible by g(x) = 4x2 + 3x -2?
Q13. What must be added to f(x) = 4x4 + 2x3 -2x2 +x - 1, so that the resulting polynomial is divisible
by g(x) = x2 +2x -3?
Q14. If the polynomial x4 + 2x3 +8x2 +12x+18 is divided by another polynomial x 2 +5, the
remainder comes out to be px+ q. Find the values of ' p' and ' q'?
Q15. If α, β, γ be zeros of the polynomial 6x3 + 3x2 -5x+1, then find the value of α-1 + β -1 + γ -1?
Q16. If α, β are the two zeros of the polynomial f(y) = y2 - 8y +a and α2 + β2 = 40, find the value of
‘a’? LONG ANSWER TYPE QUESTIONS
Q17. Obtain all other zeros of the polynomial 2x4 - 9x 3 + 5x 2 + 3x - 1, if two of its zeros are 2-√3
and 2 + √3? (CBSE 2018)
Q18. Find the zeros of the polynomial f(x) = x3 - 5x2 -2x +24, if it is given that the product of its two
zeros is 12?
Q19. If α, β are zeros of the quadratic polynomial f(x) = 2x2 + 11x + 5, find a) α4 + β4 b)1/α +1/β -2αβ
Q20. If the zeros of the polynomial f(x) = x3 – 3x2 - 6x + 8 are of the form a-b, a, a+b, then find all the
zeros.
Answers
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Answer:
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Correct option is
C
c and a have the same sign
Given that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.
=> Value of the discriminant(D) has to be zero.
=>b2−4ac=0
=>b2=4ac
Since. L.H.S b2 cannot be negative, thus, R.H.S. can also be never negative.
Therefore, a and c must be of the same sign
Step-by-step explanation:


Answer
Open in answr app
Correct option is
C
c and a have the same sign
Given that the zeros of the quadratic polynomial ax2+bx+c,c=0 are equal.
=> Value of the discriminant(D) has to be zero.
=>b2−4ac=0
=>b2=4ac
Since. L.H.S b2 cannot be negative, thus, R.H.S. can also be never negative.
Therefore, a and c must be of the same sign
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