Question

if p and q are zeroes of 3x^2+2x-9 then the value of p-q is

Answer 1

Step-by-step explanation:

3x²+2x-9

sum of root= -b/a

p+q= -2/3

product of root= c/a

pq= -9/3

pq= -3

(p+q)²= (p-q)²+4pq

(-2/3)²= (p-q)²+4•(-3)

4/9= (p-q)²-12

4/9+12= (p-q)²

112/9= (p-q)²

√(112/9)= p-q

√(4×4×7/3×3)= p-q

4√7/3= p-q

#666

Answer 2

SOLUTION

GIVEN

p and q are zeroes of 3x² + 2x - 9

TO DETERMINE

The value of p - q

EVALUATION

Here it is given that p and q are zeroes of

3x² + 2x - 9

$\displaystyle \sf \: p + q = - \frac{2}{3}$

$\displaystyle \sf \: p q = - \frac{9}{3} = - 3$

Now

$\displaystyle \sf {(p - q)}^{2} = {(p + q)}^{2} - 4pq$

$\displaystyle \sf \implies {(p - q)}^{2} = \frac{4 + 108}{9}$

$\displaystyle \sf \implies {(p - q)}^{2} = \frac{112}{9}$

$\displaystyle \sf \implies {(p - q)}^{} = \frac{4 \sqrt{7}}{3}$

FINAL ANSWER

$\displaystyle \sf {(p - q)}^{} = \frac{4 \sqrt{7}}{3}$

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