Question

Find the zeros of the quadratic polynomial x square -7 and verify the relationship between the zeroes and the cofficients..​

Answer 1

Answer:

x²-7 here a=1 ,b=0, c=-7

Answer 2

S O L U T I O N :

We have quadratic polynomial p(x) = x² - 7 & zero of the polynomial p(x) = 0

$\underline{\underline{\tt{Using\:\:by\:\:factorisation\:\:method\::}}}$

→ x² - 7 = 0

→ x² = 7

→ x = ±√7

→ x = √7 or x = -√7

∴ α = √7 & β = -√7 are the two zeroes of the polynomial .

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

• a = 1
• b = 0
• c = -7

Now,

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

$\mapsto\tt{\alpha + \beta = \dfrac{-b}{a} = \bigg\lgroup \dfrac{Coefficient\:of\:x}{Coefficient\:of\:x^{2}}\bigg\rgroup}$

$\mapsto\tt{\sqrt{7} + ( -\sqrt{7}) = \dfrac{-0}{1} }$

$\mapsto\tt{\sqrt{7} -\sqrt{7} = 0 }$

$\mapsto\bf{0 = 0}$

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

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

$\mapsto\tt{\sqrt{7} \times ( -\sqrt{7}) = \dfrac{-7}{1} }$

$\mapsto\tt{-\sqrt{7 \times 7} = -7}$

$\mapsto\bf{-7 = -7}$

Thus,

The relationship between zeroes & coefficient are verified .