Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
The roots of the equation x² - 7x + 12 = 0 are:
3,4
3,−4
2,6
1,12
3,4
Find two numbers whose product is 12 and sum is 7. Clearly, 3 and 4 satisfy both conditions (3×4=12 and 3+4=7), so the roots are the opposite signs: 3 and 4.
Quadratic equation x² - 7x + 12 = 0
x=2a−b±b2−4ac
Find two numbers whose product is 12 and sum is 7. Clearly, 3 and 4 satisfy both conditions (3×4=12 and 3+4=7), so the roots are the opposite signs: 3 and 4.
Students often confuse the signs of the roots when factoring or forget that roots of (x−p)(x−q)=0 are p and q, leading to selecting negative roots.
Identify coefficients
Compare the given equation x2−7x+12=0 with the standard quadratic form ax2+bx+c=0 to get a=1, b=−7, and c=12.
a=1,b=−7,c=12
Apply factorization
Split the middle term −7x into −3x and −4x such that their product is 12x2 and sum is −7x. Rewrite the equation as x2−3x−4x+12=0.
x(x−3)−4(x−3)=0
Solve for x
Factor out (x−3) to get (x−3)(x−4)=0, which yields the roots x=3 and x=4.
x=3 or x=4
A is correct because the roots of the equation x2−7x+12=0 are 3 and 4.
Understanding the relationship between roots and coefficients (Vieta's formulas) helps quickly verify solutions in algebra and higher-order polynomial equations.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants