Doubts
Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents
Sign in to save progress →
Doubts
Sign in

Quadratic Equation and Inequalities question

2022 · 29 Jul · Shift 2 · Q37
Guest · try one question or challengeGuest · try one question or challenge
  1. PYQ Library
  2. /JEE Main
  3. /Mathematics
  4. /Quadratic Equation and Inequalities
  5. /2022 · 29 Jul · Shift 2 · Q37

Quadratic Equation and Inequalities question

2022 · 29 Jul · Shift 2 · Q37

JEE MainMathematicsQuadratic Equation and InequalitiesNumerical+4 / −1
Let α,β(α>β)\alpha, \beta(\alpha\gt \beta)α,β(α>β) be the roots of the quadratic equation x2−x−4=0.x^{2}-x-4=0 .x2−x−4=0. If Pn=αn−βnP_{n}=\alpha^{n}-\beta^{n}Pn​=αn−βn, n∈Nn \in \mathrm{N}n∈N, then P15P16−P14P16−P152+P14P15P13P14\frac{P_{15} P_{16}-P_{14} P_{16}-P_{15}^{2}+P_{14} P_{15}}{P_{13} P_{14}}P13​P14​P15​P16​−P14​P16​−P152​+P14​P15​​ is equal to ‾\underline{\hspace{2cm}}​.
Numerical answer
PreviousNext

More from Quadratic Equation and Inequalities

  • Let α be a root of the equation 1 + x2 + x4 = 0. Then, the value of α 1011 + α 2022 −α 3033 is equal to :2022 · MCQ
  • Let S1​={x∈R−{1,2}:−2+3x−x2(x+2)(x2+3x+5)​≥0} and S2​={x∈R:32x−3x+1−3x+2+27≤0}. Then, S1​∪S2​ is…2022 · MCQ
  • Let S be the set of all integral values of α for which the sum of squares of two real roots of the quadratic equation 3x2+(α−6)x+(α+3)=0 is minimum. Then S :2022 · MCQ
  • The numbers of pairs (a, b) of real numbers, such that whenever α is a root of the equation x2 + ax + b = 0, α 2 − 2 is also a root of this equation, is :2021 · MCQ
  • Let f(x) be a polynomial of degree 3 such that f(k)=−k2​ for k = 2, 3, 4, 5. Then the value of 52 − 10f(10) is equal to :2021 · Numerical
  • The value of 4+5+4+5+4+......∞1​1​1​1​ is :2021 · MCQ
  • The value of 3+4+3+4+3+....∞1​1​1​1​ is equal to2021 · MCQ
  • If α and β are the distinct roots of the equation x2+(3)1/4x+31/2=0, then the value of α96(α12−1)+β96(β12−1) is equal to :2021 · MCQ