1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. (i) x2 – 2x – 8 (ii) 4s2 – 4s + 1 (iii) 6×2 – 3 –…
2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i) (1over4), 1 (ii) (sqrt{2}),(1 over 3) (iii) 0, (sqrt{5}) (iv) 1, 1 (v)…
1. The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case. Previous Next Class 10 Polynomials Exercise 2.2 1. Find the zeroes of the…
1. Matrices A and B will be inverse of each other only if (A) AB=BA (B) AB=BA=0 (C) AB=0, BA=I (D) AB=BA=I. Previous Next Class 12 Matrices Miscellaneous Exercise 1. If A and B are symmetric matrices, prove that AB–BA is…
11. If A is square matrix such that (A^2=A), then ((I+A)^3–7A) is equal to(A) A(B) I–A(C) I(D) 3A Previous Next Class 12 Matrices Miscellaneous Exercise 1. If A and B are symmetric matrices, prove that AB–BA is a skew symmetric…
10. If the matrix A is both symmetric and skew symmetric, then (A) A is a diagonal matrix(B) A is a zero matrix(C) A is a square matrix(D) None of these Previous Next Class 12 Matrices Miscellaneous Exercise 1. If…
9. If (A=begin{bmatrix}α&β \ γ &-αend{bmatrix}) is such that (A^2=I), then (A) (1+α^2+βγ=0)(B) (1-α^2+βγ=0)(C) (1-α^2-βγ=0)(D) (1+α^2-βγ=0). Previous Next Class 12 Matrices Miscellaneous Exercise 1. If A and B are symmetric matrices, prove that AB–BA is a skew symmetric matrix. 2.…
8. Find the matrix X so that (Xbegin{bmatrix}1&2&3 \ 4&5&6 end{bmatrix}=)(begin{bmatrix}-7&-8&-9 \ 2&4&6 end{bmatrix}). Previous Next Class 12 Matrices Miscellaneous Exercise 1. If A and B are symmetric matrices, prove that AB–BA is a skew symmetric matrix. 2. Show that…
7. A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: Market Products I 10,000 2,000 18,000 II 6,000 20,000 8,000 (a) If unit sale prices of x, y and z…
6. Find x, if (A=begin{bmatrix}x&-5&-1end{bmatrix}) (begin{bmatrix}1&0&2 \0&2&1\2&0&3 end{bmatrix})(begin{bmatrix}x\4\1 end{bmatrix}=O). Previous Next Class 12 Matrices Miscellaneous Exercise 1. If A and B are symmetric matrices, prove that AB–BA is a skew symmetric matrix. 2. Show that the matrix B’AB is symmetric…
