Polynomials — Questions & Answers

Sample questions from Polynomials

1. Q1. The zeroes of the polynomial 6x² − 7x − 3 are:

   • A.3/2 and 1/3
   • B.−3/2 and 1/3
   • C.3/2 and −1/3✓
   • D.−3/2 and −1/3
   Solution

   6x² − 7x − 3 = (2x − 3)(3x + 1), giving x = 3/2 and x = −1/3.

2. Q2. If zeroes of 2x²−7x+3 are α,β, then αβ is:

   • A.3/2✓
   • B.−3/2
   • C.7/2
   • D.−7/2
   Solution

   αβ=c/a=3/2.

3. Q3. The remainder when p(x)=2x²+5x−3 is divided by x+2 is:

   • A.−5✓
   • B.5
   • C.3
   • D.−3
   Solution

   p(−2)=8−10−3=−5.

4. Q4. If the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and −3, then:

   • A.a = −7, b = −1
   • B.a = 5, b = −1
   • C.a = 2, b = −6
   • D.a = 0, b = −6✓
   Solution

   Sum of zeroes = −1 = −(a + 1) gives a = 0, and product = −6 = b.

5. Q5. If α,β are zeroes of x²−4x+1, then α²+β² is:

   • A.14✓
   • B.16
   • C.2
   • D.18
   Solution

   α²+β²=(α+β)²−2αβ=16−2=14.

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