石and-4227. If two zeroes of the polynomial32. Given2+7x-19x2 14x +30

1.	石and-4227. If two zeroes of the polynomial32. Given2+7x-19x2 14x +30 areV2 and-2, then find all the zeroespolynomform a,number13 F121290]
Answer» Zeroes of polynomial are√2 and -√2Factor will be(x-√2)(x+√2)=(x²-2) now, dividing the polynomial with this factor, x²-2)2x⁴ +7x³ -19x² -14x +30(2x²+7x-15 2x⁴ -4x² - + 0 7x³-15x²-14x+30 7x³ -14x - + 0 -15x 0 +30 -15x +30 + - 0 0 So, the factors are (x²-2)(2x²+7x-15)=(x²-2)(2x²+10x -3x -15)=(x²-2)[2x(x+5)-3(x+5)]=(x²-2)(x+5)(2x-3) so, other zeroes are -5 and 3/2

石and-4227. If two zeroes of the polynomial32. Given2+7x-19x2 14x +30 areV2 and-2, then find all the zeroespolynomform a,number13 F121290]

Answer»

Zeroes of polynomial are√2 and -√2Factor will be(x-√2)(x+√2)=(x²-2)

now, dividing the polynomial with this factor,

x²-2)2x⁴ +7x³ -19x² -14x +30(2x²+7x-15 2x⁴ -4x² - + 0 7x³-15x²-14x+30 7x³ -14x - + 0 -15x 0 +30 -15x +30 + - 0 0

So, the factors are (x²-2)(2x²+7x-15)=(x²-2)(2x²+10x -3x -15)=(x²-2)[2x(x+5)-3(x+5)]=(x²-2)(x+5)(2x-3)

so, other zeroes are -5 and 3/2