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Relations between roots and coefficients, nature of roots Revision for JEE

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Revise Relations between roots and coefficients, nature of roots by covering every subtopic once, drilling formulas, then solving 12+ timed MCQs with full solutions.

Use this Relations between roots and coefficients, nature of roots revision checklist before mocks and the final exam. Reinforce concepts with 12+ syllabus-aligned MCQs on Goodmarks.

Revision checklist

  1. 1.Core idea: Relations between roots and coefficients, nature of roots
  2. 2.Relates to other subtopics in Complex Numbers and Quadratic Equations
  3. 3.Argand diagram, modulus, argument
  4. 4.Roots of quadratics, relation with coefficients
  5. 5.Master Relations between roots and coefficients, nature of roots definitions and standard results
  6. 6.Solve 20 timed MCQs for Relations between roots and coefficients, nature of roots

Syllabus context

Part of Complex Numbers and Quadratic Equations in JEE Main Mathematics.

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Q1MathsUnit 2: Complex Numbers and Quadratic Equations
If x+1x=4,x+\frac{1}{x}=4, then x4+1x4x^{4}+\frac{1}{x^{4}} is equal to
Q2MathsUnit 2: Complex Numbers and Quadratic Equations
If the product of two numbers is 10 and their sum is 7,7, which is the greatest of the two numbers?
Q3MathsUnit 2: Complex Numbers and Quadratic Equations
The zeros of the polynomial n3+9n2+n^{3}+9 n^{2}+ 23n+1523 n+15 are a−d,aa-d, a and a+d.a+d . What is the value of 'a'?
Q4MathsUnit 2: Complex Numbers and Quadratic Equations
Discriminant of the equation −3x2+-3 x^{2}+ 2x−8=02 x-8=0 is
Q5MathsUnit 2: Complex Numbers and Quadratic Equations
If the sum of the roots of the equation ax2+bx+c=0a x^{2}+b x+c=0 is equal to sum of the squares of their reciprocals, then bc2,ca2,ab2b c^{2}, c a^{2}, a b^{2} are in
Q6MathsUnit 2: Complex Numbers and Quadratic Equations
If x−y=7x-y=7 and x3−y3=133;x^{3}-y^{3}=133 ; find: the value of xyx y
Q7MathsUnit 2: Complex Numbers and Quadratic Equations
Find p∈Rp \in R for x2−px+p+3=0x^{2}-p x+p+3=0 has
Q8MathsUnit 2: Complex Numbers and Quadratic Equations
Assertion Let equations ax2+bx+c=a x^{2}+b x+c= 0(a,b,c∈R)&x2+2x+5=0\mathbf{0}(\boldsymbol{a}, \boldsymbol{b}, \boldsymbol{c} \in \boldsymbol{R}) \& \boldsymbol{x}^{2}+\mathbf{2} \boldsymbol{x}+\mathbf{5}=\mathbf{0} have common root, then a+cb=13\frac{\boldsymbol{a}+\boldsymbol{c}}{\boldsymbol{b}}=\frac{\mathbf{1}}{\mathbf{3}} Reason If both roots of Ax2+Bx+K1=0&A x^{2}+B x+K_{1}=0 \& A′x2+B′x+K2=0\boldsymbol{A}^{\prime} \boldsymbol{x}^{2}+\boldsymbol{B}^{\prime} \boldsymbol{x}+\boldsymbol{K}_{2}=\mathbf{0} are identical then⁡AA1=BB1=K1K2( where A,B,K1\operatorname{then} \frac{\boldsymbol{A}}{\boldsymbol{A}_{1}}=\frac{\boldsymbol{B}}{\boldsymbol{B}_{1}}=\frac{\boldsymbol{K}_{1}}{\boldsymbol{K}_{2}}\left(\text { where } \boldsymbol{A}, \boldsymbol{B}, \boldsymbol{K}_{1}\right. and A′,B,′K2∈R)\left.A^{\prime}, B,^{\prime} K_{2} \in R\right)

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Follow the checklist on this page, revise formulas daily, and attempt mixed MCQs every 2–3 days.

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