Question

10x2-14x-12 find sum of zeros and product of zeros
.​

Answer 1

Explanation.

⇒ equation :-  10x²-14x-12.

To find the zeroes and product of zeroes.

⇒ 10x²-14x-12=0.

sum of zeroes of quadratic equation

⇒ α +β = -b/a

⇒ α+β = -(-14)/10

⇒ α+β = 7/5.     ............(1).

product of zeroes of quadratic equation.

⇒ αβ = c/a

⇒ αβ = (-12)/10

⇒ αβ = -6/5.   .......(2).

                         

more information.

(1) = [ D < 0  or b² - 4ac < o ] ⇒ roots are imaginary.

(2) = [ D = 0 or b² - 4ac = 0 ] ⇒ roots are real and equal.

(3) = [ D > 0 or b² -  4ac > 0 ] ⇒ roots are real and unequal.

Answer 2

Answer :-

Sum of zeros = $\sf \frac{-b}{a}$

Product of zeros = $\sf \frac{c}{a}$

For the given equation -

• a = 10
• b = -14
• c = -12

$\sf Sum \: of \:zeros = \frac{-b}{a} \\ \\= \sf\frac{-(-14)}{10} \\ \\=\sf \frac{14}{10}\\\\ = \sf\frac{7}{5}$

$\sf Product\: of \:zeros = \frac{c}{a} \\\\ = \sf\frac{-12}{10} \\\\= \sf\frac{-6}{5}$

Hence, Sum of zeros = 7/5

Product of zeros = -6/5