Correct Answer: The equation has two real solutions.<\/strong><\/p>\n\n\n\n Consider the given equation: To solve for xxx, we first isolate the squared term:(x\u2212a)2=b(x – a)^2 = b(x\u2212a)2=b<\/p>\n\n\n\n Since both aaa and bbb are positive real numbers<\/strong>, bbb is greater than zero. This means the right-hand side of the equation is a positive number. Taking the square root of both sides:x\u2212a=\u00b1bx – a = \\pm\\sqrt{b}x\u2212a=\u00b1b\u200b<\/p>\n\n\n\n This gives two distinct solutions:x=a+bandx=a\u2212bx = a + \\sqrt{b} \\quad \\text{and} \\quad x = a – \\sqrt{b}x=a+b\u200bandx=a\u2212b\u200b<\/p>\n\n\n\n These are two different real numbers<\/strong> because b\\sqrt{b}b\u200b is a positive number. Therefore, a+ba + \\sqrt{b}a+b\u200b and a\u2212ba – \\sqrt{b}a\u2212b\u200b are not equal.<\/p>\n\n\n\n This equation represents a horizontal shift of a basic quadratic function. The graph of (x\u2212a)2(x – a)^2(x\u2212a)2 is a parabola that opens upward and has its vertex at x=ax = ax=a. When we subtract bbb, the entire graph shifts downward by bbb units. Because bbb is positive, the vertex drops below the x-axis, ensuring that the parabola intersects the x-axis at two distinct points<\/strong>. These points correspond to the two real solutions we found earlier.<\/p>\n\n\n\n This is an important feature of quadratic equations:<\/p>\n\n\n\n Since b>0b > 0b>0, the equation always has two real solutions<\/strong> for all positive real values of aaa and bbb.<\/p>\n\n\n\n Consider the equation (x-a)^2 – b = 0, where a and b are both positive real numbers. Write a statement about the number of real solutions for the equation that must be true. The Correct Answer and Explanation is: Correct Answer: The equation has two real solutions. Explanation Consider the given equation:(x\u2212a)2\u2212b=0(x – a)^2 – […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-26714","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26714","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=26714"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26714\/revisions"}],"predecessor-version":[{"id":26716,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26714\/revisions\/26716"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26714"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26714"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26714"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation<\/h3>\n\n\n\n
(x\u2212a)2\u2212b=0(x – a)^2 – b = 0(x\u2212a)2\u2212b=0<\/p>\n\n\n\n\n
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