Question

if x=23 and x=-3 are roots of quadratic ax2 +7x+b=0.find the value of a and b​

Answer 1

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Answer 2

Aɴsᴡᴇʀ

we have,

• roots of quadratic equation are 23 and -3

• sum of roots = 23 + (-3) = 20

• product of roots = 23 × (-3) = -69

and we know that,

if a quadratic equation is ax² + bx + c = 0

then,

$\underline{ \boxed{ \bold{sum \: of \: roots = \frac{ - b}{ \: a} }}}$

and

$\underline{ \boxed{ \bold{product \: of \: roots = \frac{c}{a} }}}$

__________________________

now, compare the given quadratic equation to ax² + bx + c = 0

• ax² + 7x + b = 0

then,

• a = a
• b = 7
• c = b

now,

we have,

• sum of roots = 20
• product of roots = -69

$\bold{: \implies 20 = \frac{ - 7}{a} } \\ \\ \bold{ : \implies\boxed{\bold{ a = \frac{ - 7}{20} }}}$

$\bold{ : \implies - 69 = \frac{b}{a} } \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies - 69a = b} \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies - 69 \times \frac{ -7 }{20} = b} \\ \\ \bold{ : \implies\boxed{\bold{ b = \frac{483}{20} }}} \: \: \: \: \: \: \: \: \: \: \: \:$

• a = -7/20
• b = 483/20

hence, value of a is -7/20 and value of b is 483/20