HSC Science Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions

A quadratic polynomial has one of its zeros `1 + sqrt(5)` and it satisfies p(1) = 2. Find the quadratic polynomial

If α and β are the roots of the quadratic equation `x^2 + sqrt(2)x + 3` = 0, form a quadratic polynomial with zeroes `1/α, 1/β`

If one root of k(x − 1)² = 5x − 7 is double the other root, show that k = 2 or −25

If the difference of the roots of the equation 2x² − (a + 1)x + a − 1 = 0 is equal to their product, then prove that a = 2

Find the condition that one of the roots of ax² + bx + c may be negative of the other

Find the condition that one of the roots of ax² + bx + c may be thrice the other

Find the condition that one of the roots of ax² + bx + c may be reciprocal of the other

If the equations x² − ax + b = 0 and x² − ex + f = 0 have one root in common and if the second equation has equal roots, then prove that ae = 2(b + f)

Discuss the nature of roots of − x² + 3x + 1 = 0

Discuss the nature of roots of 4x² − x − 2 = 0

Discuss the nature of roots of 9x² + 5x = 0

Without sketching the graph, find whether the graph of the following function will intersect the x-axis and if so in how many points
y = x² + x + 2

Without sketching the graph, find whether the graph of the following function will intersect the x-axis and if so in how many points
y = x² − 3x − 7

Without sketching the graph, find whether the graph of the following function will intersect the x-axis and if so in how many points
y = x² + 6x + 9

Write f(x) = x² + 5x + 4 in completed square form

Solve 2x² + x – 15 ≤ 0

Solve – x² + 3x – 2 ≥ 0

Choose the correct alternative:
Find a so that the sum and product of the roots of the equation 2x² + (a − 3)x + 3a − 5 = 0 are equal is

Choose the correct alternative:
If a and b are the roots of the equation x² − kx + 16 = 0 and satisfy a² + b² = 32, then the value of k is

Choose the correct alternative:
The number of solutions of x² + |x − 1| = 1 is