Question

find the zeroes of polynomial x2-7x-30=0 and verify the relation between sum and product of zeroe​

Answer 1

Answer:

Hope it Works.......... ☺

Answer 2

Solution :

We have quadratic polynomial p(x) = x² - 7x - 30 = 0, so we get find zeroes by factorization method :

$\longrightarrow\sf{x^{2} -7x-30=0}\\\\\longrightarrow\sf{x^{2} +3x-10x-30=0}\\\\\longrightarrow\sf{x(x+3)-10(x+3)=0}\\\\\longrightarrow\sf{(x+3)(x-10)=0}\\\\\longrightarrow\sf{x+3=0\:\:\:Or\:\:\:x-10=0}\\\\\longrightarrow\bf{x=-3\:\:\:Or\:\:\:x=10}$

∴ We have α = -3 & β = 10 are the zeroes of polynomial .

As we know that given polynomial compared with ax² + bx + c;

• a = 1
• b = -7
• c = -30

Now;

$\underline{\mathcal{SUM\:OF\:THE\:ZEROES\::}}$

$\mapsto\tt{\alpha +\beta =\dfrac{-b}{a} =\bigg\lgroup\dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2} } \bigg\rgroup}\\\\\\\mapsto\tt{-3+10=\dfrac{-(-7)}{1} }\\\\\\\mapsto\bf{7=7}$

$\underline{\mathcal{PRODUCT\:OF\:THE\:ZEROES\::}}$

$\mapsto\tt{\alpha \times \beta =\dfrac{c}{a} =\bigg\lgroup\dfrac{Constant\:term}{Coefficient\:of\:x^{2} } \bigg\rgroup}\\\\\\\mapsto\tt{-3\times 10=\dfrac{-30}{1} }\\\\\\\mapsto\bf{-30=-30}$

Thus;

The relationship between zeroes & coefficient are verified .