**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.

**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%.