alleryFind k if x²+3x+k leaves remainder −2 when divided by x.
- 2
- −5
- 5
- −2
Show answer and solution
Correct answer: D. −2
Division by x leaves the constant term k, which must be −2.
ICSE Class 10 Algebra: Equations, Inequations & Matrices — practice questions — page 7
Explore 212 free Algebra: Equations, Inequations & Matrices questions in ICSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 181–210 of 212.
Find k if x²+3x+k leaves remainder −2 when divided by x.Read the answer and worked solution →2x³+ax²+bx−2 has factors x−1 and x+1. Find (a,b).Read the answer and worked solution →x²+ax+b leaves 3 on x−1 and 7 on x+1. Find (a,b).Read the answer and worked solution →x³+ax²+bx+5 leaves equal remainders on x−1 and x+1. Find b.Read the answer and worked solution →For (2x−1) to divide 2x³+kx²−5x+2, k must beRead the answer and worked solution →The complete factorisation of x³−4x²+5x−2 isRead the answer and worked solution →If x+2 divides x³+3x²−4, the quotient isRead the answer and worked solution →Which value is a zero of 6x³−x²−4x−1?Read the answer and worked solution →A monic cubic has zeros 0, 2 and −3. Which polynomial is it?Read the answer and worked solution →A cubic has zeros 1, −1, 2 and leading coefficient 3. Its constant term isRead the answer and worked solution →What must be added to x³−2x+5 to make x−1 a factor?Read the answer and worked solution →Which identity proves x+1 is a factor of x³+1?Read the answer and worked solution →The largest integer that satisfies x <= 7 isRead the answer and worked solution →Which of the following is an inequation?Read the answer and worked solution →Solving an inequation means findingRead the answer and worked solution →When both sides of an inequation are multiplied by a negative number,Read the answer and worked solution →Solve 2 x - 1 < 5, then x belongs toRead the answer and worked solution →Solve -3 x < 9, then x belongs toRead the answer and worked solution →Solve 3 (x + 1) - 2 (x - 1) > 7. Then x belongs toRead the answer and worked solution →Solve (x - 1)/2 + 3 < 6. Then x belongs toRead the answer and worked solution →Solve the double inequation 2 < x + 1 <= 5. Then x belongs toRead the answer and worked solution →Solve -4 < 2 - x <= 1 over integers.Read the answer and worked solution →The solution of 5 - 2 x > 1 isRead the answer and worked solution →Solve 5 (x - 2) >= 15, then x belongs toRead the answer and worked solution →The largest integer x satisfying 3 x - 4 < 2 x + 5 isRead the answer and worked solution →Solve (x + 2)/3 - (x - 1)/2 <= 1. Then x belongs toRead the answer and worked solution →Solve 2 x + 5 > 11, then x belongs toRead the answer and worked solution →Solve -2 (x - 3) <= 4. Then x belongs toRead the answer and worked solution →Solve (2 x - 5) / 3 >= 1 over integers.Read the answer and worked solution →Solve x + 3 > 5, then x belongs toRead the answer and worked solution →
Worked practice questions
2x³+ax²+bx−2 has factors x−1 and x+1. Find (a,b).
- (2,−2)
- (2,2)
- (−2,−2)
- (−2,2)
Show answer and solution
Correct answer: A. (2,−2)
Substitution of 1 and −1 gives a+b=0 and a−b=4, hence a=2 and b=−2.
x²+ax+b leaves 3 on x−1 and 7 on x+1. Find (a,b).
- (−2,−4)
- (−2,4)
- (2,−4)
- (2,4)
Show answer and solution
Correct answer: B. (−2,4)
The equations 1+a+b=3 and 1−a+b=7 give a=−2 and b=4.
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