Question

7. The sum of roots of the quadratic equation 3x? - 9x + 5 = 0 is ---
(a) 3
(b) 6
(c)-3
(d) 2
.​

Answer 1

Question

The sum of roots of the quadratic equation 3x² - 9x + 5 = 0 is ____

a. 3

b. 6

c. -3

d. 2

Solution

Let α , β be zeroes of the polynomial 3x² - 9x + 5 .

Compare given poly. with ax² + bx + c ,

• a = 3  ,  b = - 9  ,  c = 5

Sum of zeroes , α + β = -b/a

$:\implies \sf \alpha +\beta=-\dfrac{(-9)}{3}$

$:\implies \sf \alpha +\beta =\dfrac{9}{3}$

$:\implies \sf \pink{\alpha + \beta =3}\ \; \bigstar$

Option a

More Info

Product of zeroes ,

$:\implies \sf \alpha \beta =\dfrac{c}{a}$

For a cubic polynomial ax³ + bx² + cx + d ,

Sum of zeroes ,

$:\implies \sf \alpha + \beta + \gamma =-\dfrac{b}{a}$

Sum of product of zeroes ,

$:\implies \sf \alpha \beta +\beta \gamma + \gamma \alpha =\dfrac{c}{a}$

Product of zeroes ,

$:\implies \sf \alpha \beta \gamma =-\dfrac{d}{a}$

Answer 2

$\bf{\gray{\underbrace{\blue{GIVEN:-}}}}$

• $\bf\pink{3x^2\:-\:9x\:+\:5\:=\:0\:}$

$\bf{\gray{\underbrace{\blue{TO\:FIND:-}}}}$

• The sum of roots of the given quadratic equation .

$\bf{\gray{\underbrace{\blue{SOLUTION:-}}}}$

$\orange\bigstar\:\bf{\red{\overbrace{\underbrace{\purple{Sum\:of\:roots\:=\:\dfrac{-Coefficient\:of\:x}{Coefficient\:of\:x^2}\:}}}}}$

• $\bf\blue{Coefficient\:of\:x}$ = -9

• $\bf\blue{Coefficient\:of\:x^2}$ = 3

➳ Sum of roots = $\bf{\dfrac{-(-9)}{3}\:}$

➳ Sum of roots = $\rm{\dfrac{9}{3}\:}$

➳ Sum of roots = $\bf\orange{3}$

$\red\therefore$ (a) The sum of roots of the quadratic equation "3x² - 5x + 9" is "3"