Advertisements
Advertisements
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
Concept: Solutions of Quadratic Equations by Factorization
Sum of the areas of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares ?
Concept: Solutions of Quadratic Equations by Completing the Square
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
Concept: Solutions of Quadratic Equations by Factorization
Which of the following is not a quadratic equation?
Concept: Quadratic Equations
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
Concept: Nature of Roots of a Quadratic Equation
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
Concept: Nature of Roots of a Quadratic Equation
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
Concept: Solutions of Quadratic Equations by Factorization
If x = –2 is the common solution of quadratic equations ax2 + x – 3a = 0 and x2 + bx + b = 0, then find the value of a2b.
Concept: Solutions of Quadratic Equations by Factorization
If the quadratic equation ax2 + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.
Concept: Nature of Roots of a Quadratic Equation
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
Concept: Nature of Roots of a Quadratic Equation
If α and β are roots of the quadratic equation x2 – 7x + 10 = 0, find the quadratic equation whose roots are α2 and β2.
Concept: Solutions of Quadratic Equations by Factorization
Find the discriminant of the quadratic equation 4x2 – 5 = 0 and hence comment on the nature of roots of the equation.
Concept: Relationship Between Discriminant and Nature of Roots
Find the value of 'p' for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
Concept: Nature of Roots of a Quadratic Equation
Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.
Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.
Concept: Nature of Roots of a Quadratic Equation
Find the discriminant of the quadratic equation `3x^2 - 2x + 1/3` = 0 and hence find the nature of its roots.
Concept: Nature of Roots of a Quadratic Equation
Find the roots of the quadratic equation x2 – x – 2 = 0.
Concept: Solutions of Quadratic Equations by Factorization
Find the value of k for which the roots of the quadratic equation 5x2 – 10x + k = 0 are real and equal.
Concept: Nature of Roots of a Quadratic Equation
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
Concept: Nature of Roots of a Quadratic Equation
In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
