Write the coefficients of x 2 in each of the following:
(i) 2 + x 2 + x
(ii) 2 – x 2 + x 3
(iii) \(\frac{π }{ 2}\) x2 + x
(iv) √2 x -1
(i) 2 + x2 + x
In the above expression, the coefficient of x2 is 1.
(ii) 2 - x2 + x3
In the above expression, the coefficient of x2 is -1.
(iii) \(\frac{ π}{2}\)x2 + x
In the above expression, the coefficient of x2 is π/2.
(iv) √2x - 1, or 0.x2+√2x - 1
In the above expression, the coefficient of x2 is 0.
Write the degree of each of the following polynomials:
(i) 5x 3 + 4x 2 + 7x (ii) 4 – y 2 (iii) 5t – √7 (iv) 3.
Classify the following as linear, quadratic and cubic polynomials:
(i) x 2 + x (ii) x – x 3 (iii) y + y 2 + 4 (iv) 1 + x (v) 3t (vi) r 2 (vii) 7x 3
Find the zero of the polynomial in each of the following cases:
(i) p(x) = x + 5 (ii) p(x) = x – 5 (iii) p(x) = 2x + 5 (iv) p(x) = 3x – 2 (v) p(x) = 3x
(vi) p(x) = ax, a ≠ 0 (vii) p(x) = cx + d, c ≠ 0, c, d are real numbers.
(i) The kind of person the doctor is (money, possessions)
(ii) The kind of person he wants to be (appearance, ambition)
ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see Fig. 7.17). Prove that
(i) ∆ ABD ≅ ∆ BAC
(ii) BD = AC
(iii) ∠ ABD = ∠ BAC.
