POLYNOMIAL, CLASS 10 MATHEMATICS скачать в хорошем качестве

POLYNOMIAL, CLASS 10 MATHEMATICS

Relationship between Zeroes and Coefficients of a Polynomial 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and coefficients. (i) x²-2x-8 (ii) 4s²-4s+1 (iii) 6 x²-3-7x (iv) 4u²+ 8 u (v) t²-15 (vi) 3 x²-x-4 2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (i) 1/4, -1 (ii) √2, 1/3 (iii) 0, √5 (iv) 1, 1 (v) -1/4, 1/4, (vi) 4, 1. In this video we have discussed 1. Polynomials of degree 1, 2 and 3 i.e. linear, quadratic and cubic. 2. A quadratic polynomial in x with real coefficients is of the form ax²+bx+c, where a. b, c are real numbers with a not equal to 0. 3. The zeroes of a polynomial p(x) are precisely the x- coordinates of the points, where the graph of y= p(x) intersects the x-axis. 4. A quadratic polynomial can have at most two zeroes and a cubic polynomial can have at most 3 zeroes. 5. If α and β are the zeroes of the quadratic polynomial ax²+bx+c, then α+β = -b/a and α β =c/a 6. If α, β and γ are the zeroes of the cubic polynomial ax³+bx²+ c x+d, then α+β+γ = -b/a α β +β γ+ γ α =c/a αβγ = -d/a