Kindly answer these questions correctly with steps . wrong answers will be reported
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1. The polynomial has zero at 5x=-3, so x=-3/5 is the solution.
2. BODMAS → Exponent first!
→ 4×2³-8
→ 4×8-8
→ 24
3. x=2 will satisfy x²-3x+a=0.
Exponent first!
→ 2²-3×2+a=0
→ 4-6+a=0
→ a=2
4. P(-2)=0 and P(3)=0
- P(-2)=0
→ 2×(-2)³-(-2)²-2a+b=0
→ -16-4-2a+b=0
→ -2a+b=20 ... (1)
- P(3)=0
→ 2×(3)³-3²+3a+b=0
→ 54-9+3a+b=0
→ 3a+b=-45 ... (2)
∴The solutions are a=-13 and b=-6.
5. Without actually dividing, we can split the terms.
→ 2x³-2x²-2x-5
→ (2x³-2x²)-(2x-2)-7
→ 2x²(x-1)-2(x-1)-7
→ (2x²-2)(x-1)-7 = BQ + R
∴The quotient is 2x²-2, the remainder is -7.
6. x³+6x²-x
→ x(x²+6x-1) = BQ
∴The quotient is x²+6x-1.
7. x²-y²
→ (x+y)(x-y) = BQ
∴The quotient is x-y.
8. A polynomial of nth degree has exactly n roots.
∴4 roots
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