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Q1. Find the values of a and b so that the polynomial x3- ax2+ 7x - b has (x + 1) and (x - 2) as factors.

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Q3. If f(x) = -x4+ 2x3+ 5x2- 6x + 7 and g(x) = 2x - 5. What would be the remainder if f(x) is divided by g(x)?
Q4. When p(x) = 2x4+ x3+ 3x2- sx + t is divided by (x - 1) and (x + 2), the remainders are respectively 4 and 22. Determine the remainder when p(x) is divided by (x + 1).
Q5. The polynomials 3x3+ ax2- 8 and 2x2- x - a when divided by (x + 1) leave remainders R1and R2respectively. Find the value of a, if 2R1- R2= 2.
Q6. If the polynomials p(x) = bx3- 5x2- 5x + 10 and q(x) = x4- 3x2 + b leave the same remainder when divided by (x - 3), find the value of b.
Q1. If a ≠ b but a2 = 5a − 3 and b2 = 5b − 3 then the equation whose roots are a/b and b/a is
Q2. The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b2 + c?
Q3. The roots of the equation x2 + px + q = 0 are 1 and 2. The roots of the equation qx2 - px + 1 = 0 must be:
Q4. If one of the roots of equation x2 + mx + n = 0 is the square of the other, then which of the following condition will be true?
Q5. If ‘α’ and ‘β’ are roots of a quadratic equation such that, 1/α + 1/β = 8/15 and α2 – β2 = 16, then find that quadratic equation.
Q7. Find the quadratic equation if the sum of roots and product of roots of the equation are 3/5 and -1/7 respectively?
Q8. ax2- bx + 15= 0, if (5/2) & 3 are the roots of the given quadratic equation then find the value of (a + b).
Q9. If p, q are the roots of the Quadratic equation ax2+ bx + c = 0. Then what is the equation whose roots are 1/p, 1/q ?
Q10. Ifα andβ are the roots of the equation x2 - 11x + 24 = 0, find the equation having the rootsα + 2 andβ + 2.
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Q1. In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. 3x2+ 14x + 16 = 0II. 3y2+ 22y + 24 = 0
Q2. In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. x2 – 8x + 15 = 0II. 12y2 – 19y + 5 = 0
Q3. In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. x2= 16II. y2= 49
Q5. In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.I. 2x2–9x–5 = 0II. 4y2+ 4y + 1 = 0
Q7. If AB and CD are two chords of a circle intersected at point O. If CO = 4 cm and OD = 3.75 cm and AB = 8 cm then find the length of smaller between AO and BO.
Q8. If the marked price of an article is Rs. 800 and The selling price of the same article after two equal successive discount is Rs. 512, then find each discount%.

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Q10. The cost price of 15 dozen mangoes is Rs. 1335 and the selling price of 5 dozen mangoes is Rs. 495, then find Profit/Loss%.