If equations a x 2 + b x + c = 0 ,   a ,   b ,   c ∈ R ,   a ≠ 0 and 2 x 2 + 3 x + 4 = 0 have a common root, then a : b : c equals :

Question

If equations a x 2 + b x + c = 0 , &#160; a , &#160; b , &#160; c &#8712; R , &#160; a &#8800; 0 and 2 x 2 + 3 x + 4 = 0 have a common root, then a : b : c equals :

Aicharya · Accepted Answer

a x 2 + b x + c = 0 ....(i) 2 x 2 + 3 x + 4 = 0 ....(ii) For equation (ii), D = 9 - 4 2 4 = - 23 &#60; 0 Roots are complex conjugates. &#8658; Both roots are common in equation (i) and (ii). &#8756;&#160;&#160;&#160; a 2 = b 3 = c 4 &#8658;&#160;a &#160;:&#160; b &#160;:&#160; c &#160;: :&#160; 2 &#160;:&#160; 3 &#160;:&#160; 4

If equations a x 2 + b x + c = 0 ,   a ,   b ,   c ∈ R ,   a ≠ 0 and 2 x 2 +…

Solution

If equations a x 2 + b x + c = 0 , &#160; a , &#160; b , &#160; c &#8712; R , &#160; a &#8800; 0 and 2 x 2 +…

Solution

If equations a x 2 + b x + c = 0 , a , b , c ∈ R , a ≠ 0 and 2 x 2 +…