Question

3. If a and b are the roots of the equation 3x -5x+2 = 0 , then find the values of

Answer 1

p(x)= 3x^2-5x+2=0,

here ,

a=3 , b= -5 and c= 2

we know that,

sum of zeroes= -b/a

$\alpha + \beta = \frac{5}{3}$
also,

product of zeroes= c/a

$\alpha \times \beta = \frac{2}{3}$
now,

$\frac{ \alpha }{ \beta } + \frac{ \beta }{ \alpha } = \frac{ { \alpha }^{2} + { \beta }^{2} }{ \alpha \times \beta }$
using identity a^2+b^2= (a+b)^2-2ab

$\frac{ \frac{5}{3} ^{2} - \frac{4}{3} }{ \frac{2}{3} } \\ \\ = 7 \div \frac{2}{3} = \frac{21}{2}$

Answer 2

Solution :

Here I am using roots m , n instead

of Alfa, and beta.

Given Quadratic equation ,

3x² - 5x + 2 =0

Splitting the middle terms , we get

=> 3x² - 3x - 2x + 2 = 0

=> 3x( x - 1 ) - 2( x - 1 ) = 0

=> ( x - 1 )( 3x - 2 ) = 0

=> x - 1 = 0 or 3x - 2 = 0

x = 1 or x = 2/3

Therefore ,

m = 1 , n = 2/3

i ) ( m² + n² )/mn

= [ 1² + (2/3)²]/( 1 × 2/3 )

= [ 1 + 4/9 ]/(2/3 )

= ( 13/9 )/( 2/3 )

= 13/6

ii ) m - n

= 1 - 2/3

= ( 3 - 2 )/3

= 1/3

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