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Standard X

Mathematics

Roots of Quadratic Equation

If a and b ar...

Question

If a and b are the roots of $x^{2} - 3 x + p = 0$ and c,d are roots of $x^{2} - 12 x + q = 0$ .
Then find the sum of a,b,c,d

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Solution

Given $a$ and $b$ are the roots of $x^{2} - 3 x + p = 0$
$∴$ $a + b = 3$
Also $c$ and $d$ are roots of $x^{2} - 12 x + q = 0$
$∴$ $c + d = 12$
Sum of $a + B + c + d = 4 + 12 = 15$

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Similar questions

Q. If

A

and

B

are the roots of

x^{2} - 3 x + p = 0

and

C, D

are the roots of

x^{2} - 12 x + q = 0

, where

a, b, c, d

form a

G P

then prove that

q + p : q - p = 17 : 15

If a and b are the roots $x^{2} - 3 x + p = 0$ and c, d are roots of $x^{2} - 12 x + q = 0$ , where a, b, c, d form a G.P. Prove that $(q + p) : (q - p) = 17 : 15$ .

Q. If a and b are the roots of

x^{2} - 3 x + p = 0

and c and d are roots of the equation

x^{2} - 12 x + q

where

a, b, c a n d d

forms a G.P. Prove that

(q + p) : (q - p) = 17 : 15

Q. Let a and b be roots of

x^{2} - 3 x + p = 0

and let c and d be roots of

x^{2} - 12 x + q = 0

where a,b,c,d form increasing G.P. then the ratio of (q + p) : (q - p) is equal to

Q. Let

a

and

b

be the roots of

x^{2} - 3 x + p = 0

and let

c

and

d

be the roots of

x^{2} - 12 x + q = 0

, where

a, b, c

form an increasing G.P. Then the ratio of

q + p : q - p

is equal to

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If a and b are the roots of x2−3x+p=0 and c,d are roots of x2−12x+q=0.Then find the sum of a,b,c,d

Given a and b are the roots of x2−3x+p=0∴ a+b=3Also c and d are roots of x2−12x+q=0∴ c+d=12Sum of a+B+c+d=4+12=15

If a and b are the roots of $x^{2} - 3 x + p = 0$ and c,d are roots of $x^{2} - 12 x + q = 0$ .
Then find the sum of a,b,c,d

Given $a$ and $b$ are the roots of $x^{2} - 3 x + p = 0$
$∴$ $a + b = 3$
Also $c$ and $d$ are roots of $x^{2} - 12 x + q = 0$
$∴$ $c + d = 12$
Sum of $a + B + c + d = 4 + 12 = 15$