Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and their coefficient ​

Answer 1

Step-by-step explanation:

here is the solution my friend

Hope it helps!!!

Answer 2

$\large\bf\underline{Question:-}$

find the zeroes of quadratic polynomial p(x) 2x²- 7 and verify the relationship between the zeroes and their coefficient .

━━━━━━━━━━━━━━━━━

$\large\bf\underline{Given:-}$

• p(x) = 2x² - 7

$\large\bf\underline {To \: find:-}$

• zeroes of the given polynomial.

• relationship between the zeroes and coefficients.

$\huge\bf\underline{Solution:-}$

p(x) = 2x² - 7

$\dashrightarrow \rm \: {2x}^{2} - 7 = 0 \\ \\ \dashrightarrow \rm \: 2 {x}^{2} = 7 \\ \\ \dashrightarrow \rm \: {x}^{2} = \frac{7}{2} \\ \\ \dashrightarrow \rm \: x = \pm\sqrt{ \frac{7}{2} }$

So, the zeroes of the given polynomial are:-

$\bullet \: \bf \: x = \sqrt{ \frac{7}{2} } \: or \: x = - \sqrt{ \frac{7}{2} }$

Let α and β are the zeroes of the given polynomial.

Let :-

• ★ α = √7/2
• ★ β = -√7/2

➝ p(x) = 2x² - 7

• a = 2
• b = 0
• c = -7

$\large\blacktriangleright \bf \: sum \: of \: zeroes = \frac{ - b}{a}$

$\longrightarrow \rm \: \frac{ \sqrt{7} }{ \sqrt{2} } + ( - \frac{ \sqrt{7} }{ \sqrt{2} } ) = \frac{0}{2} \\ \\ \longrightarrow \rm \: \frac{ \sqrt{7} - \sqrt{7} }{ \sqrt{2} } = 0 \\ \\ \longrightarrow \rm \: 0 = 0$

$\large\blacktriangleright \bf \: product \: of \: zeroes = \frac{ c}{a}$

$\longrightarrow \rm \: \frac{ \sqrt{7} }{ \sqrt{2} } \times ( - \frac{ \sqrt{7} }{ \sqrt{2} } ) = \frac{ - 7}{2} \\ \\ \longrightarrow \rm \: \frac{ - 7}{2} = \frac{ - 7}{2}$

LHS = RHS

hence relationship is verified.