Question

5. Find the zeroes of the quadratic polynomial x² - 7x - 18 and verify the
relationship between the zeroes and the coefficients.​

Answer 1

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

• p(x) = x² - 7x - 18

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

• zeroes of the given polynomial.

• relationship between the zeroes and coefficients.

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

• ➣ p(x) = x² - 7x -18

➝ x² + 2x - 9x - 18

➝ x(x + 2) -9(x + 2)

➝ (x - 9)(x + 2)

➝ x = 9 or x = -2

$\large \: \underbrace{ \dag\bf \: Verification \: \: \: \: }$

• ➣ Zeroes are 9 and -2

Relationship between the zeroes and coefficients.

• p(x) = x² - 7x -18
• a = 1
• b = -7
• c = -18

• ≫ Sum of zeroes = -b/a

»» 9 + (-2) = -(-7)/1

»» 7 = 7

• ≫ Product of zeroes = c/a

»» 9 × (-2) = -18/1

»» -18 = -18

LHS = RHS

Hence relationship is verified.

$\boxed{\begin{minipage}{10cm}\\</p><p>\bf\: Sum of zeroes = - coefficient of x/coefficient of x^2\\\bf \:Product \:of\: zeroes = constant term/coefficient \:of\: x^2 \end{minipage}}$

Answer 2

$\huge \underline \red{answer}$

° p(x) = x² - 7x -18

➝ x² + 2x - 9x - 18

➝ x(x + 2) -9(x + 2)

➝ (x - 9)(x + 2)

➝ x = 9 or x = -2

THANK YOU