Question

Find the zeroes of the quadratic polynomial Xsquare minus 2X minus 3
If possible please write in a paper and send a photo

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore x=3\:and\:-1}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• We have to find the zeroes of given polynomial.

$\underline \bold{Given : } \\ \implies x \in( {x}^{2} - 2x - 3 = 0) \\ \\ \underline \bold{To \: Find: } \\ \implies x = ?$

• According to given question :

$\bold{ {x}^{2} - 2x - 3x = 0} \\ \\ \bold{Using \: quadratic \: formula : } \\ \implies x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ \implies x = \frac{ - ( - 2) \pm \sqrt{( - 2)^{2} - 4 \times 1 \times ( - 3) } }{2 \times 1} \\ \\ \implies x = \frac{2 \pm \sqrt{4 + 12} }{2} \\ \\ \implies x = \frac{2 \pm \sqrt{16} }{2} \\ \\ \implies x = \frac{2 \pm 4}{2} \\ \\ \bold{\implies x = 3 \: and \: - 1} \\ \\ \bold{Middle \: term \: spliting : } \\ \implies {x}^{2} - 2x - 3 = 0 \\ \\ \implies {x}^{2} -3x + x - 3 = 0 \\ \\ \implies x(x - 3) + 1(x - 3) = 0 \\ \\ \implies (x + 1)(x - 3) = 0 \\ \\ \bold{\implies x = 3 \: and \: - 1}$

Answer 2

Solution

from given question need to find the zeroes of the quadratic polynomial x² - 2x - 3

we can use the formula

The formula is called "quadratic formula"

x = - b ± √b² - 4ac / 2 a

x = - ( - 2 ) ± √( - 2 )² - 4 × 1 × ( - 3) / 2 × 1

x = 2 ± √4 + 12 / 2

x = 2 ± √2 + 4 / 2

x = ( 3 ) , ( - 1 )

Now Spliting the middle term

x² - 2x - 3 = 0

x² - 3x + x - 3 = 0

x * (x - 3) + 1 (x + 3) = 0

(x + 1) (x - 3) = 0

Answer = x = 3 and 1 are the zeroes of the quadratic polynomial and also Value of x = (3 ) , ( - 1)